necessary conditions for ternary algebras ternary algebras constructed from ternary commutators or as we call them ternutators defined as the alternating sum of products of three operators have been shown to satisfy cubic identities as necessary conditions for their existence here we examine the situation where we permit identities not solely constructed from ternutators or nested ternutators and we find that in general these impose additional restrictions for example the anti commutators or commutators of the operators must obey some linear relations among themselves

an envelope for malcev algebras we prove that for every malcev algebra m there exist an algebra u m and a monomorphism m u m of m into the commutator algebra u m such that the image of m lies into the alternative center of u m and u m is a universal object with respect to such homomorphisms the algebra u m in general is not alternative but it has a basis of poincare birkhoff witt type over m and inherits some good properties of universal enveloping algebras of lie algebras in particular the elements of m can be characterized as the primitive elements of the algebra u m with respect to the diagonal homomorphism u m u m u m an extension of ado iwasawa theorem to malcev algebras is also proved

locally conformal kahler manifolds with potential a locally conformally kahler lck manifold m is one which is covered by a kahler manifold widetilde m with the deck transformation group acting conformally on widetilde m if m admits a holomorphic flow acting on widetilde m conformally it is called a vaisman manifold neither the class of lck manifolds nor that of vaisman manifolds is stable under small deformations we define a new class of lck manifolds called lck manifolds with potential which is closed under small deformations all vaisman manifolds are lck with potential we show that an lck manifold with potential admits a covering which can be compactified to a stein variety by adding one point this is used to show that any lck manifold m with potential dim m 3 can be embedded into a hopf manifold thus improving similar results for vaisman manifolds ornea and verbitsky math ann 332 121 143 2005

n ary algebras a review with applications this paper reviews the properties and applications of certain n ary generalizations of lie algebras in a self contained and unified way these generalizations are algebraic structures in which the two entries lie bracket has been replaced by a bracket with n entries each type of n ary bracket satisfies a specific characteristic identity which plays the role of the jacobi identity for lie algebras particular attention will be paid to generalized lie algebras which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized jacobi identity and to filippov or n lie algebras which are defined by fully antisymmetric n brackets that satisfy the filippov identity three lie algebras have surfaced recently in multi brane theory in the context of the bagger lambert gustavsson model because of this filippov algebras will be discussed at length including the cohomology complexes that govern their central extensions and their deformations it turns out that whitehead s lemma extends to all semisimple n lie algebras when the skewsymmetry of the lie or n lie algebra bracket is relaxed one is led to a more general type of n algebras the n leibniz algebras these will be discussed as well since they underlie the cohomological properties of n lie algebras the standard poisson structure may also be extended to the n ary case we shall review here the even generalized poisson structures whose generalized jacobi identity reproduces the pattern of the generalized lie algebras and the nambu poisson structures which satisfy the filippov identity and determine filippov algebras finally the recent work of bagger lambert and gustavsson on superconformal chern simons theory will be briefly discussed emphasis will be made on the appearance of the 3 lie algebra structure and on why the a4 model may be formulated in terms of an ordinary lie algebra and on its nambu bracket generalization

higher identities for the ternary commutator we use computer algebra to study polynomial identities for the trilinear operation a b c abc acb bac bca cab cba in the free associative algebra it is known that a b c satisfies the alternating property in degree 3 no new identities in degree 5 a multilinear identity in degree 7 which alternates in 6 arguments and no new identities in degree 9 we use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11 the only irreducible representations of dimension 400 with new identities correspond to partitions 25 1 and 24 13 and have dimensions 132 and 165 we construct an explicit new multilinear identity for partition 25 1 and we demonstrate the existence of a new non multilinear identity in which the underlying variables are permutations of a2b2c2d2e2f

a solution to an open problem for wave equations with generalized wentzell boundary conditions in this paper we solve an open problem put forward by a favini g r goldstein j a goldstein and s romanelli concerning the mixed problem for wave equations with generalized wentzell boundary conditions as a consequence we also develop the previous wellposedness result regarding the mixed problem for heat equations with generalized wentzell boundary conditions

spectral analysis and an area preserving extension of a piecewise linear intermittent map we investigate the spectral properties of a one dimensional piecewise linear intermittent map which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point we explicitly derive generalized eigenvalues and eigenfunctions of the frobenius perron operator of the map for classes of observables and piecewise constant initial densities and it is found that the frobenius perron operator has two simple real eigenvalues 1 and ensuremath lambda d ensuremath 1 0 and a continuous spectrum on the real line 0 1 from these spectral properties we also found that this system exhibits a power law decay of correlations this analytical result is found to be in a good agreement with numerical simulations moreover the system can be extended to an area preserving invertible map defined on the unit square this extended system is similar to the baker transformation but does not satisfy hyperbolicity a relation between this area preserving map and a billiard system is also discussed

on the disk theorem we construct an example of a 2 dimensional stein normal space x with one singular point x0 such that x x0 is simply connected and it satisfies the disk condition this answers a question raised by fornaess and narasimhan we also prove that any increasing union of stein open sets contained in a stein space of dimension 2 satisfies the disk condition starting from the above example we exhibit without using deformation theory a new type of 2 dimensional holes which cannot be filled

hopf algebras with triality in this joint work with g benkart and j m perez izquierdo we revisit and extend the constructions of glauberman and doro on groups with triality and moufang loops to hopf algebras we prove that the universal enveloping algebra of any lie algebra with triality is a hopf algebra with triality this allows a new construction of the universal enveloping algebras of malcev algebras our work relays on the approach of grishkov and zavarnitsine to groups with triality

on deformations of the witt n algebra we reinvestigate the two different q witt algebras and construct their n algebras in one case the super version is also presented moreover we investigate the central extensions and present the super q virasoro n algebras for the n even case we study a toy model for the q virasoro constraints a q witt n algebra is discussed in this model

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

the simple non lie malcev algebra as a lie yamaguti algebra the simple 7 dimensional malcev algebra m is isomorphic to the irreducible sl 2 c module v 6 with binary product x y x y defined by the sl 2 c module morphism 2v 6 v 6 combining this with the ternary product x y z x y z defined by the sl 2 c module morphism 2v 6 v 2 sl 2 c gives m the structure of a generalized lie triple system or lie yamaguti algebra we use computer algebra to determine the polynomial identities of low degree satisfied by this binary ternary structure

free akivis algebras primitive elements and hyperalgebras free akivis algebras and primitive elements in their universal enveloping algebras are investigated it is proved that subalgebras of free akivis algebras are free and that finitely generated subalgebras are finitely residual decidability of the word problem for the variety of akivis algebras is also proved the conjecture of k h hofmann and k strambach problem 6 15 in topological and analytic loops in quasigroups and loops theory and applications series in pure mathematics o chein h o pflugfelder and j d h smith eds vol 8 pp 205 262 heldermann verlag berlin 1990 on the structure of primitive elements is proved to be not valid and a full system of primitive elements in free nonassociative algebra is constructed finally it is proved that every algebra b can be considered as a hyperalgebra that is a system with a series of multilinear operations that plays a role of a tangent algebra for a local analytic loop where the hyperalgebra operations on b are interpreted by certain primitive elements

identities of cayley dickson algebras abstract we compute the identities and the central identities of degree 6 of the cayley dickson algebras our process can be used to compute identities of higher degree we assume a field of characteristic 0 or greater than the degree of the identities studied our identities are homogeneous multilinear polynomials

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

on a class of n leibniz deformations of the simple filippov algebras we study the problem of infinitesimal deformations of all real simple finite dimensional filippov or n lie algebras considered as a class of n leibniz algebras characterized by having an n bracket skewsymmetric in its n 1 first arguments we prove that all n 3 simple finite dimensional filippov algebras fas are rigid as n leibniz algebras of this class this rigidity also holds for the leibniz deformations of the semisimple n 2 filippov i e lie algebras the n 3 simple fas however admit a nontrivial one parameter infinitesimal 3 leibniz algebra deformation we also show that the n 3 simple filippov algebras do not admit nontrivial central extensions as n leibniz algebras of the above class

modular invariant of quantum tori the quantum modular invariant j qt of 2r is defined as a discontin uous pgl2 z invariant multi valued map using the distance to the nearest integer function k k for 2 q it is shown that j qt 1 and for quadratic irrationalities pari gp experiments suggest that j qt is a finite set in the case of the golden mean we produce explicit formulas involving weighted versions of the rogers ramanujan functions for the experimental supremum and infimum we then define a universal modular invariant j a mod c as a continuous and single valued map of ultrasolenoids such that 1 the classical modular invariant is a quotient of the re striction of j to a subsolenoid mod cl a mod fibering over the classical moduli space of elliptic curves and 2 the quantum modular invariant is a quotient of the restric tion of j to a subsolenoid mod qt a mod fibering over the moduli space of elliptic curves equipped with a kronecker foliation

locating resonances for axiom a dynamical systems for a class of differentiable dynamical systems called axiom a systems it has been shown by pollicott and the author that correlation functions have fourier transforms which are meromorphic in a strip the poles or resonances are however not easy to locate this note reviews the results which are known and discusses a simple model where the position of resonances can be estimated the effect of noise is also discussed

the colored symmetric and exterior algebras abstract we study colored generalizations of the symmetric algebra and its koszul dual the exterior algebra the symmetric group s n acts on the multilinear components of these algebras while s n acts trivially on the multilinear components of the colored symmetric algebra we use poset topology techniques to understand the representation on its koszul dual we introduce an s n poset of weighted subsets that we call the weighted boolean algebra and we prove that the multilinear components of the colored exterior algebra are s n isomorphic to the top cohomology modules of its maximal intervals we use a technique of sundaram to compute group representations on cohen macaulay posets to give a generating formula for the frobenius series of the colored exterior algebra we exploit that formula to find an explicit expression for the expansion of the corresponding representations in terms of irreducible s n representations we show that the two colored koszul dual algebras are koszul in the sense of priddy

identities for algebras of matrices over the octonions abstract this paper describes all the identities of degree 7 satisfied by algebras of 2 2 matrices over the octonions there are three cases 1 the full matrix algebra under the usual matrix product 2 the algebra of hermitian matrices under the symmetric product and 3 the algebra of skew hermitian matrices under the antisymmetric product in case 1 we present seven new identities in degree 7 which were discovered by a computer search but which are proved to hold for matrices with entries in any alternative ring in case 2 we recover the identities of vasilovsky in degrees 5 and 6 for the special jordan algebra of a nondegenerate symmetric bilinear form in case 3 we describe a computational proof that there are no identities in degree 7 which are not implied by anticommutativity

on the compactification of hyperconcave ends and the theorems of siu yau and nadel we show that the pseudoconcave holes of some naturally arising class of manifolds called hyperconcave ends can be filled in including the case of complex dimension two as a consequence we obtain a stronger version of the compactification theorem of siu yau and extend nadel s theorems to dimension two

the cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points we compute the poincare polynomial and the cohomology algebra with rational coefficients of the manifold m n of real points of the moduli space of algebraic curves of genus 0 with n labeled points this cohomology is a quadratic algebra and we conjecture that it is koszul we also compute the 2 local torsion in the cohomology of m n as was shown by the fourth author the cohomology of m n does not have odd torsion so that the above determines the additive structure of the integral homology and cohomology further we prove that the rational homology operad of m n is the operad of 2 gerstenhaber algebras which is closely related to the hanlon wachs operad of 2 lie algebras generated by a ternary bracket finally using drinfeld s theory of quantization of coboundary lie quasibialgebras we show that a large series of representations of the quadratic dual lie algebra l n of h m n q associated to such quasibialgebras factors through the the natural projection of l n to the associated graded lie algebra of the prounipotent completion of the fundamental group of m n this leads us to conjecture that the said projection is an isomorphism which would imply a formula for lower central series ranks of the fundamental group on the other hand we show that the spaces m n are not formal starting from n 6

graded polynomial identities of the jordan superalgebra of a bilinear form letwsp 2q w0 p w1 2q be a direct sum of two vector spaces of dimensionpand 2q respectively over a fieldkof characteristic zero p 2 3 q 1 2 and let x y be a nondegenerate bilinear form onwsp 2qwhich is symmetric onw0 p and skew symmetric onw1 2q and such that w0 p w1 2q w1 2q w0 p 0 then the vector spacebsp 2q k wsp 2qequipped with the product v u v u u v k v u wsp 2q is a simple jordan superalgebra withk w0 p as its even component andw1 2q as the odd one in this paper explicit finite bases for graded polynomial identities of the series of jordan superalgebrasbsp 2q p 2 3 q 1 2 are found

contractions of filippov algebras we introduce in this paper the contractions gc of n lie or filippov algebras g and show that they have a semidirect structure as their n 2 lie algebra counterparts as an example we compute the nontrivial contractions of the simple an 1 filippov algebras by using the inonu wigner and the generalized weimar woods contractions of ordinary lie algebras we compare in the g an 1 simple case the lie algebras liegc the lie algebra of inner endomorphisms of gc with certain contractions lie g iw and lie g w w of the lie algebra lieg associated with g

multi operator brackets acting thrice we generalize an identity first found by bremner for nambu 3 brackets for odd n brackets built from associative operator products we show that for any fixed a when totally antisymmetrized over all the bs

compactification of complete kahler manifolds of negative ricci curvature soit m une variete de kahler complete de dimension m et soit la forme de kahler on suppose 1 ric 0 2 m est tres fortement m 2 pseudoconcave 3 le recouvrement universel de m est de stein alors m est biholomorphe a une variete quasiprojective

on the definitions of nucleus for dialgebras abstract malcev dialgebras were introduced recently by bremner peresi and sanchez ortega in the present paper we continue their study by introducing the notion of the generalized alternative dinucleus of a 0 dialgebra a general conjecture about the speciality of malcev dialgebras in terms of this dinucleus is formulated in the last section we introduce the appropriate generalization of the associative nucleus for dialgebras and prove an analogue of kleinfeld s theorem for the setting of dialgebras

identities for the ternary commutator abstract this paper classifies all identities of degree 7 satisfied by the ternary commutator in an associative ternary algebra seven is the lowest degree for which non trivial identities exist these identities are ternary generalizations of the jacobi identity for lie algebras

alternating quaternary algebra structures on irreducible representations of sl2 c abstract we determine the multiplicity of the irreducible representation v n of the simple lie algebra sl 2 c as a direct summand of its fourth exterior power 4 v n the multiplicity is 1 resp 2 if and only if n 4 6 resp n 8 10 for these n we determine the multilinear polynomial identities of degree 7 satisfied by the sl 2 c invariant alternating quaternary algebra structures obtained from the projections 4 v n v n we represent the polynomial identities as the nullspace of a large integer matrix and use computational linear algebra to find the canonical basis of the nullspace

the differential zeta function for axiom a attractors closed orbit of least period x t an important problem is to construct the meromorphic extensions for these zeta functions a detailed knowledge of the domain of s gives information on the long term behaviour of the flow for example this is a standard approach to deriving asymptotic formulae for closed orbits cf 9 for the case of geodesic flows on surfaces of constant negative curvature the zeta function is known to have a meromorphic extension to the entire complex plane unfortunately an obstruction to a general theory along these lines is the existence of examples of axiom a flows for which d s does not have a meromorphic extension to c in a recent article william parry proposed a modified definition of a zeta function for axiom a attractors he defined the differential zeta function by ns s h i e s t l where the least period x x of a closed orbit is replaced by the expansion xu t along the unstable manifold around the orbit 8 parry also defined the useful notion of a synchronized flow i e one for which the measure of maximal entropy and the srb measure coincide the following remark is taken from page 273 of his article when the flow is synchronized the zeta functions coincide this is the case for example with a geodesic flow on a surface of constant negative curvature one wonders whether synchronization has something to do with the very desirable features of the zeta function of such a geodesic flow in this article we shall give a solution to parry s question which shows that in many cases du s has a meromorphic extension to the entire complex plane our main result can be stated as follows

piecewise linear model of self organized hierarchy formation the bonabeau model of self organized hierarchy formation is studied by using a piecewise linear approximation to the sigmoid function simulations of the piecewise linear agent model show that there exist two level and three level hierarchical solutions and that each agent exhibits a transition from nonergodic to ergodic behaviors furthermore by using a mean field approximation to the agent model it is analytically shown that there are asymmetric two level solutions even though the model equation is symmetric asymmetry is introduced only through the initial conditions and that linearly stable and unstable three level solutions coexist it is also shown that some of these solutions emerge through supercritical pitchfork like bifurcations in invariant subspaces existence and stability of the linear hierarchy solution in the mean field model are also elucidated

identities for generalized lie and jordan products on totally associative triple systems abstract we determine the identities of degree 9 satisfied by the new ternary operations abc bca cab acb bac cba symmetric sum abc bca cab acb bac cba alternating sum and abc bca cab cyclic sum on every triple system satisfying the total associativity identities abc de a bcd e ab cde these new operations are ternary analogs of the lie and jordan products the identities they satisfy may be regarded as ternary versions of the jacobi and jordan identities

generation of localization in a discrete chain with periodic boundary conditions numerical and analytical results we study the generation of localization in a discrete chain composed of n subsystems and periodic boundary conditions strongly localized motions are studied that is time periodic motions where nearly all of the energy is spatially confined to a single subsystem for varying n numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in phase spatially extended solution however in the limit as n rightarrow infty the bifurcation point tends to infinity and a smooth transition from localization to nonlocalization occurs we then present an analytic technique to complement the numerical results it is based on the matching local asymptotic expansions of a solution branch using pade approximants this leads to global analytic representations of the considered solutions valid over the entire range of the control parameter

the method weak lefschetz theorems and the topology of kahler manifolds in no nori studied the fundamental group of complements of nodal curves with ample normal bundle in smooth projective surfaces the main tool was the following weak lefschetz theorem theorem nori suppose u x is a local biholomorphism from a connected complex manifold u into a connected smooth projective variety x of dimension at least 2 and u contains a connected effective divisor y with compact support and ample normal bundle then for every zariski open subset z of x the image of 1 1 z in 1 z is of finite index

stickiness in hamiltonian systems from sharply divided to hierarchical phase space we investigate the dynamics of chaotic trajectories in simple yet physically important hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures we show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one parameter families of marginally unstable periodic orbits and is characterized by an exponent ensuremath gamma 2 for the asymptotic power law decay of the distribution of recurrence times generic perturbations lead to systems with hierarchical phase space where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and cantori in this case we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws depending on the relative contribution of the primary and secondary structures of the hierarchy numerical verification of our main results are provided for area preserving maps mushroom billiards and the newly defined magnetic mushroom billiards

spectral characterization of anomalous diffusion of a periodic piecewise linear intermittent map abstract for a piecewise linear version of the periodic map with anomalous diffusion the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the frobenius perron fp operator are explicitly derived the evolution of the averages is controlled by real eigenvalues as well as continuous spectra terminating at the unit circle appropriate scaling limits are shown to give a normal diffusion if the reduced map is in the stationary regime with normal fluctuations a levy flight if the reduced map is in the stationary regime with levy type fluctuations and a transport of ballistic type if the reduced map is in the non stationary regime

nilpotent sabinin algebras abstract in this paper we establish several basic properties of nilpotent sabinin algebras namely we show that nilpotent sabinin algebras 1 can be integrated to produce nilpotent loops 2 satisfy an analogue of the ado theorem 3 have nilpotent lie envelopes we also give a new set of axioms for sabinin algebras these axioms reflect the fact that a complementary subspace to a lie subalgebra in a lie algebra is a sabinin algebra finally we note that the non associative version of the jennings theorem produces a version of the ado theorem for loops whose commutator associator filtration is of finite length

jordan triples and operads abstract we study the jordan triple systems in terms of operads we give the description of the operad of these ternary algebras as a quadratic operad and prove that the quadratic dual of this operad is the operad of partially antisymmetric partially associative ternary algebras nous etudions les systemes triples de jordan en termes d operades nous donnons une description de l operade quadratique de ces algebres ternaires et montrons que son dual quadratique est l operade des algebres ternaires partiellement associatives partiellement antisymetriques

ternary derivations of finite dimensional real division algebras abstract we present for each n 1 2 4 8 a group acting on the set of all division algebra structures on r n and an invariant the lie algebra of ternary derivations for this action an exploration of these structures is conducted in terms of this new invariant obtaining simple descriptions of the division algebras involved in the course of the investigation another family of algebras is considered among them the algebra sl 4 f of 4 4 traceless matrices with the symmetric product xy yx 1 2 t xy i shows an exceptional behavior

hopf quasigroups and the algebraic 7 sphere we introduce the notions of hopf quasigroup and hopf coquasigroup h generalising the classical notion of an inverse property quasigroup g expressed respectively as a quasigroup algebra kg and an algebraic quasigroup k g we prove basic results as for hopf algebras such as anti co multiplicativity of the antipode s h h that s2 id if h is commutative or cocommutative and a theory of crossed co products we also introduce the notion of a moufang hopf co quasigroup and show that the coordinate algebras k s2n 1 of the parallelizable spheres are algebraic quasigroups commutative hopf coquasigroups in our formulation and moufang we make use of the description of composition algebras such as the octonions via a cochain f introduced in 2 we construct an example k s7 z23 of a hopf coquasigroup which is noncommutative and nontrivially moufang we use hopf coquasigroup methods to study differential geometry on k s7 including a short algebraic proof that s7 is parallelizable looking at combinations of left and right invariant vector fields on k s7 we provide a new description of the structure constants of the lie algebra g2 in terms of the structure constants f of the octonions in the concluding section we give a new description of the q deformation quantum group cq s3 regarded trivially as a moufang hopf coquasigroup trivially since it is in fact a hopf algebra but now in terms of f built up via the cayley dickson process

embeddability of some strongly pseudoconvex cr manifolds we obtain an embedding theorem for compact strongly pseudoconvex cr manifolds which are boundaries of some complete hermitian manifolds we use this to compactify some negatively curved kahler manifolds with compact strongly pseudoconvex boundary an embedding theorem for sasakian manifolds is also derived

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

ternary q virasoro witt hom nambu lie algebras in this paper we construct ternary q virasoro witt algebras which q deform the ternary virasoro witt algebras constructed by curtright fairlie and zachos using su 1 1 enveloping algebra techniques the ternary virasoro witt algebras constructed by curtright fairlie and zachos depend on a parameter and are not nambu lie algebras for all but finitely many values of this parameter for the parameter values for which the ternary virasoro witt algebras are nambu lie the corresponding ternary q virasoro witt algebras constructed in this paper are also hom nambu lie because they are obtained from the ternary nambu lie algebras using the composition method for other parameter values this composition method does not yield a hom nambu lie algebra structure for q virasoro witt algebras we show however using a different construction that the ternary virasoro witt algebras of curtright fairlie and zachos as well as the general ternary q virasoro witt algebras we construct carry a structure of the ternary hom nambu lie algebra for all values of the involved parameters

spectral properties of a piecewise linear intermittent map for a piecewise linear intermittent map the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the frobenius perron operator p are explicitly derived the evolution of the averages are shown to be a superposition of the contributions from two simple eigenvalues 1 and d 1 0 and a continuous spectrum on the unit interval 0 1 of p power law decay of correlations are controlled by the continuous spectrum also the non normalizable invariant measure in the non stationary regime is shown to determine the strength of the power law decay

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

on compact complex surfaces of kahler rank one the kahler rank of compact complex surfaces was introduced by harvey and lawson in their 1983 paper on kahler manifolds as a measure of kahlerianity here we give a partial classification of compact complex surfaces of kahler rank 1 these are either elliptic surfaces or hopf surfaces or they admit a holomorphic foliation of a very special type as a consequence we give an affirmative answer to the question raised by harvey and lawson whether the kahler rank is a bimeromorphic invariant

on the compactification of concave ends let x be a complex manifold which admits a proper strictly plurisubharmonic function x a b where a b it is well known that the hausdorffness of h1 x is necessary for the existence of a stein completion of x we show that this condition is also sufficient

generalization of n ary nambu algebras and beyond the aim of this paper is to introduce n ary hom algebra structures generalizing the n ary algebras of lie type including n ary nambu algebras n ary nambu lie algebras and n ary lie algebras and n ary algebras of associative type including n ary totally associative and n ary partially associative algebras we provide examples of the new structures and present some properties and construction theorems we describe the general method allowing one to obtain an n ary hom algebra structure starting from an n ary algebra and an n ary algebra endomorphism several examples are derived using this process also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three dimensional hom nambu lie structures with diagonal homomorphism

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

triality of structurable and pre structurable algebras abstract we introduce a notion of pre structurable algebras based on the structurable algebra of allison as well as lie algebras that satisfy triality

quantum quasigroups and loops abstract quantum quasigroups and quantum loops are self dual objects providing a general framework for the nonassociative extension of quantum group techniques bialgebra reducts of hopf algebras are quantum loops while sufficient conditions are given for quantum loop structure to augment to a hopf algebra the moufang hopf algebras of benkart et al the hopf quasigroups and coquasigroups of klim majid and the coassociative h bialgebras of perez izquierdo for instance the universal enveloping algebras of sabinin algebras all form quantum loops other quantum quasigroups offer natural nonassociative extensions of hopf algebra constructions quasigroup algebras dual quasigroup algebras and quantum couples of groups with quasigroups further examples include an algebra of rooted binary trees and an algebra of skein polynomials

higher order simple lie algebras it is shown that the non trivial cocycles on simple lie algebras may be used to introduce antisymmetric multibrackets which lead to higher order lie algebras the definition of which is given their generalised jacobi identities turn out to be satisfied by the antisymmetric tensors or higher order structure constants which characterise the lie algebra cocycles this analysis allows us to present a classification of the higher order simple lie algebras as well as a constructive procedure for them our results are synthesised by the introduction of a single complete brst operator associated with each simple algebra

on lie k algebras abstract we define the notion of a lie k algebra to be a k 1 ary skew symmetric operation on a bigraded vector space which satisfies a certain relation of degree 2 k 1 the notion of lie 1 algebra coincides with the notion of lie superalgebra an ordinary lie algebra is precisely a lie 1 algebra with odd elements we show first that the boundary map in the koszul complex constructed as the koszul complex for ordinary lie algebras squares to zero we then show that the 1 nk 1 homogeneous part of the free lie k algebra with nk 1 even generators is isomorphic as an s nk 1 module to the cohomology of 1 nk 1 the poset of all partitions of nk 1 in which every block size is congruent to 1 mod k this result is analogous to a classical result relating the free lie algebra with n generators to the cohomology of the partition lattice we also construct an explicit basis for the 1 nk 1 homogeneous part of the free lie k algebra with nk 1 even generators and for the cohomology of 1 nk 1 lastly we compute the lie k algebra homology of the free lie k algebra

strongly plurisubharmonic exhaustion functions on 1 convex spaces the conclusion obtained from a stein space by blowing up finitely many points means precisely that there exist a compact analytic set s c x with d imxs 0 for any x s a stein space 14 a finite set a c y and a proper holomorphic map p x y inducing a biholomorphism x s y a and which satisfies p c x cr r following a customary terminology x is called an 1 convex space s its exceptional set and y the remmert reduction of x theorem 1 1 was conjectured by fornaess narashimhan in 5 in this paper we prove the converse

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

dynamical and transport properties in a family of intermittent area preserving maps we introduce a family of area preserving maps representing a nontrivial two dimensional extension of the pomeau manneville family in one dimension we analyze the long time behavior of recurrence time distributions and correlations providing analytical and numerical estimates we study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments finally the dynamical effects of a stochastic perturbation are considered

the x ray transform and its inversion for the series expansion basis functions in three dimensional tomography a formula for the three dimensional x ray transform and an expression for its inversion have been derived the spherical harmonics and the rotation matrices in terms of euler angles are used in the generalized fourier series expansion some properties of the transformed fourier components are discussed

nambu poisson manifolds and associated n ary lie algebroids we introduce an n ary lie algebroid canonically associated with a nambu poisson manifold we also prove that every nambu poisson bracket defined on functions is induced by some differential operator on the exterior algebra and characterizes such operators some physical examples are presented

varieties of anticommutativen ary algebras abstract a fundamental problem in the theory of n ary algebras is to determine the correct generalization of the jacobi identity this paper describes some computational results on this problem using representations of the symmetric group it is well known that over a field of characteristic 0 any variety of n ary algebras can be defined by multilinear identities in the anticommutative case it is shown that for n 8 the formula dimensional s 2 n 1 module of multilinear identities in which each term involves two n ary products i e two pairs of n ary anticommutative brackets decomposes as the direct sum of the n distinct simple modules labelled by the n partitions of 2 n 1 in which only 1 and 2 occur as parts in the cases n 3 resp n 4 the kernel of the commutator expansion map and a generator for each of the 7 resp 15 nonzero submodules are determined the paper concludes with some conjectures for n 5

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

markov tree model of transport in area preserving maps abstract transport in an area preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant cantor sets called cantori a model retaining a discrete set of cantori approaching a boundary circle gives the markov chain description of hanson cary and meiss the inclusion of cantori surrounding island chains and islands about islands etc gives a markov tree model with a slower decay rate the survival probability distribution is shown to decay asymptotically as a power law the decay exponent agrees reasonably well with the computations of karney and of chirikov and shepelyanski

ternary analogues of lie and malcev algebras abstract we consider two analogues of associativity for ternary algebras total and partial associativity using the corresponding ternary associators we define ternary analogues of alternative and assosymmetric algebras on any ternary algebra the alternating sum a b c abc acb bac bca cab cba the ternary analogue of the lie bracket defines a structure of an anticommutative ternary algebra we determine the polynomial identities of degree 7 satisfied by this operation in totally and partially associative alternative and assosymmetric ternary algebras these identities define varieties of ternary algebras which can be regarded as ternary analogues of lie and malcev algebras our methods involve computational linear algebra based on the representation theory of the symmetric group

the partially alternating ternary sum in an associative dialgebra the alternating ternary sum in an associative algebra gives rise to the partially alternating ternary sum in an associative dialgebra with products and by making the argument a the center of each term we use computer algebra to determine the polynomial identities in degree 9 satisfied by this new trilinear operation in degrees 3 and 5 we obtain these identities define a new variety of partially alternating ternary algebras we show that there is a 49 dimensional space of multilinear identities in degree 7 and we find equivalent nonlinear identities we use the representation theory of the symmetric group to show that there are no new identities in degree 9

minimal identities of octonion algebras on montre que des octonions sur un corps de caracteristique non 2 3 ou 5 ne satisfont pas d identite polynomiale de degre 4 et que les identites de degre 5 sont toutes obtenues a partir de deux polynomes

k leibniz algebras from lower order ones from lie triple to lie l ple systems two types of higher order lie l ple systems are introduced in this paper they are defined by brackets with l 3 arguments satisfying certain conditions and generalize the well known lie triple systems one of the generalizations uses a construction that allows us to associate a 2n 3 leibniz algebra l with a metric n leibniz algebra l by using a 2 n 1 linear kasymov trace form for l some specific types of k leibniz algebras relevant in the construction are introduced as well both higher order lie l ple generalizations reduce to the standard lie triple systems for l 3

on the higher order generalizations of poisson structures the characterization of the nambu poisson n tensors as a subfamily of the generalized poisson ones recently introduced and here extended to the odd order case is discussed the homology and cohomology complexes of both structures are compared and some physical considerations are made

particle like structure of lie algebras if a lie algebra structure x1d524 on a vector space is the sum of a family of mutually compatible lie algebra structures x1d524 i s we say that x1d524 is simply assembled from the x1d524 i s repeating this procedure with a number of lie algebras themselves simply assembled from the x1d524 i s one obtains a lie algebra assembled in two steps from x1d524 i s and so on we describe the process of modular disassembling of a lie algebra into a unimodular and a non unimodular part we then study two inverse questions which lie algebras can be assembled from a given family of lie algebras and from which lie algebras can a given lie algebra be assembled we develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of lie algebras the main result of our theory is that any finite dimensional lie algebra over an algebraically closed field of characteristic zero or over r can be assembled in a finite number of steps from two elementary constituents which we call dyons and

algebras hyperalgebras nonassociative bialgebras and loops abstract sabinin algebras are a broad generalization of lie algebras that include lie malcev and bol algebras as very particular examples we present a construction of a universal enveloping algebra for sabinin algebras and the corresponding poincare birkhoff witt theorem a nonassociative counterpart of hopf algebras is also introduced and a version of the milnor moore theorem is proved loop algebras and universal enveloping algebras of sabinin algebras are natural examples of these nonassociative hopf algebras identities of loops move to identities of nonassociative hopf algebras by a linearizing process in this way nonassociative algebras and hopf algebras interlace smoothly