hom lie superalgebras and hom lie admissible superalgebras the purpose of this paper is to study hom lie superalgebras that is a superspace with a bracket for which the superjacobi identity is twisted by a homomorphism this class is a particular case of graded quasi lie algebras introduced by larsson and silvestrov in this paper we characterize hom lie admissible superalgebras and provide a construction theorem from which we derive a one parameter family of hom lie superalgebras deforming the orthosymplectic lie superalgebra also we prove a z2 graded version of a hartwig larsson silvestrov theorem which leads us to a construction of a q deformed witt superalgebra

symmetry detection by generalized complex gc moments a close form solution this paper presents a unified method for detecting both reflection symmetry and rotation symmetry of 2d images based on an identical set of features i e the first three nonzero generalized complex gc moments this method is theoretically guaranteed to detect all the axes of symmetries of every 2d image if more nonzero gc moments are used in the feature set furthermore we establish the relationship between reflectional symmetry and rotational symmetry in an image which can be used to check the correctness of symmetry detection this method has been demonstrated experimentally using more than 200 images

a new approach to hom lie bialgebras abstract in this paper we introduce a new definition of a hom lie bialgebra which is equivalent to a manin triple of hom lie algebras we also introduce a notion of an o operator and then construct solutions of the classical hom yang baxter equation in terms of o operators and hom left symmetric algebras

hom structures on finite dimensional simple lie superalgebras a hom structure on a lie superalgebra is an even linear mapping which twists the super jacobi identity in this paper using kac s classification theorem and a reduction method we show that finite dimensional simple lie superalgebras over the complex field admit only the trivial hom structures that is the scalar mappings

2 cocycles on the algebra of differential operators soit c t t 1 l anneau des polynomes de laurent sur un corps complexe c soit a c t t 1 d l algebre des operateurs differentiels sur c t t 1 soit 7b u l algebre des operateurs differentiels 7b u a gl u c sur c t t 1 gl u c tout 2 cocycle sur a est equivalent a un multiple de tout 2 cocycle sur 7b u est equivalent a un multiple de

ternary hom nambu lie algebras induced by hom lie algebras the need to consider n ary algebraic structures generalizing lie and poisson algebras has become increasingly important in physics and it should therefore be of interest to study the mathematical concepts related to n ary algebras the purpose of this paper is to investigate ternary multiplications as deformations of n lie structures constructed from the binary multiplication of a hom lie algebra a linear twisting map and a trace function satisfying certain compatibility conditions we show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of hom nambu lie algebras obtained using this construction

integrals for monoidal hom hopf algebras and their applications integrals of monoidal hom hopf algebras are introduced and the existence and uniqueness of integrals for finite dimensional monoidal hom hopf algebras are investigated first then integrals are applied to the maschke type theorem for monoidal hom hopf algebras controlling the semisimplicity and separability of monoidal hom hopf algebras further monoidal hom algebras are characterized with additional frobenius property and the question when finite dimensional monoidal hom hopf algebras are frobenius is studied as applications of integrals the maschke type theorem for hom smash product is given and the morita context in the hom category h mk is constructed

yetter drinfeld modules for hom bialgebras the aim of this paper is to define and study yetter drinfeld modules over hom bialgebras a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism yetter drinfeld modules over a hom bialgebra with bijective structure map provide solutions of the hom yang baxter equation the category yhhd of yetter drinfeld modules with bijective structure maps over a hom bialgebra h with bijective structure map can be organized in two different ways as a quasi braided pre tensor category if h is quasitriangular respectively coquasitriangular the first respectively second quasi braided pre tensor category yhhd contains as a quasi braided pre tensor subcategory the category of modules respectively comodules with bijective structure maps over h

cohomology of 3 dimensional color lie algebras we develop the cohomology theory of color lie algebras due to scheunert zhang in a framework of non homogeneous quadratic koszul algebras in this approach the chevalley eilenberg complex of a color lie algebra becomes a standard koszul complex for its universal enveloping algebra providing a constructive method for computation of cohomology as an application we compute cohomologies with trivial coefficients of z 2 n graded 3 dimensional color lie algebras 2 c 2006 elsevier inc all rights reserved

one parameter formal deformations of hom lie yamaguti algebras this paper studies one parameter formal deformations of hom lie yamaguti algebras the first second and third cohomology groups on hom lie yamaguti algebras extending ones on lie yamaguti algebras are provided it is proved that first and second cohomology groups are suitable to the deformation theory involving infinitesimals equivalent deformations and rigidity however the third cohomology group is not suitable for the obstructions

hom lie 2 algebras abstract in this paper we introduce the notions of hom lie 2 algebras which is the categorification of hom lie algebras hl algebras which is the hom analogue of l algebras and crossed modules of hom lie algebras we prove that the category of hom lie 2 algebras and the category of 2 term hl algebras are equivalent we give a detailed study on skeletal hom lie 2 algebras in particular we construct the hom analogues of the string lie 2 algebras associated to any semisimple involutive hom lie algebras we also proved that there is a one to one correspondence between strict hom lie 2 algebras and crossed modules of hom lie algebras we give the construction of strict hom lie 2 algebras from hom left symmetric algebras and symplectic hom lie algebras

hom l r smash products hom diagonal crossed products and the drinfeld double of a hom hopf algebra abstract we introduce the hom analogue of the l r smash product and use it to define the hom analogue of the diagonal crossed product when h is a finite dimensional hom hopf algebra with bijective antipode and bijective structure map we define the drinfeld double of h its algebra structure is a hom diagonal crossed product and it has all expected properties namely it is quasitriangular and modules over it coincide with left right yetter drinfeld modules over h

quasi hom lie algebras central extensions and 2 cocycle like identities this paper introduces the notion of a quasi hom lie algebra or simply a qhl algebra which is a natural generalization of hom lie algebras introduced in a previous paper j t hartwig d larsson s d silvestrov deformations of lie algebras using sigma derivations math qa 0408064 quasi hom lie algebras include also as special cases color lie algebras and superalgebras and can be seen as deformations of these by maps twisting the jacobi identity and skew symmetry the natural realm for these quasi hom lie algebras is generalizations deformations of the witt algebra delta of derivations on the laurent polynomials c t t 1 we also develop a theory of central extensions for qhl algebras which can be used to deform and generalize the virasoro algebra by centrally extending the deformed witt type algebras constructed here in addition we give a number of other interesting examples of quasi hom lie algebras among them a deformation of the loop algebra less

deformations of lie algebras using σ derivations in this article we develop an approach to deformations of the witt and virasoro algebras based on sigma derivations we show that sigma twisted jacobi type identity holds for generators of such deformations for the sigma twisted generalization of lie algebras modeled by this construction we develop a theory of central extensions we show that our approach can be used to construct new deformations of lie algebras and their central extensions which in particular include naturally the q deformations of the witt and virasoro algebras associated to q difference operators providing also corresponding q deformed jacobi identities c 2005 elsevier inc all rights reserved

a twisted generalization of linear poisson brackets of hydrodynamic type we study a twisted generalization of linear poisson brackets of hydrodynamic type in which the lie bracket is replaced by a hom lie bracket with some natural additional conditions such structures correspond to the hom novikov algebras introduced by yau which is the twisted version of balinsky novikov s approach of constructing a lie algebra from a novikov algebra certain central extensions of this twisted generalization of linear poisson brackets of hydrodynamic type are obtained from the bilinear forms on their corresponding hom novikov algebras satisfying some invariance conditions finally we give some examples of the infinite dimensional hom lie algebras constructed from the hom novikov algebras in particular there is an interesting twisted generalization of the virasoro algebra

the hom yang baxter equation and hom lie algebras motivated by recent work on hom lie algebras a twisted version of the yang baxter equation called the hom yang baxter equation hybe was introduced by yau j phys a 42 165202 2009 in this paper several more classes of solutions of the hybe are constructed some of the solutions of the hybe are closely related to the quantum enveloping algebra of sl 2 the jones conway polynomial and yetter drinfel d modules under some invertibility conditions we construct a new infinite sequence of solutions of the hybe from a given one

second cohomology of q deformed witt superalgebras the purpose of this paper is to compute the second adjoint cohomology group of q deformed witt superalgebras they are hom lie superalgebras obtained by q deformation of witt lie superalgebra that is one considers derivations instead of classical derivations

o operators on hom lie algebras o operators also known as relative rota baxter operators on lie algebras have several applications in integrable systems and the classical yang baxter equations in this article we study o operators on hom lie algebras we define a cochain complex for o operators on hom lie algebras with respect to a representation any o operator induces a hom pre lie algebra structure we express the cochain complex of an o operator in terms of the specific hom lie algebra cochain complex if the structure maps in a hom lie algebra and its representation are invertible then we can extend the above cochain complex to a deformation complex for o operators by adding the space of zero cochains subsequently we study formal deformations of o operators on regular hom lie algebras in terms of the deformation cohomology in the end we deduce deformations of s rota baxter operators of weight 0 and skew symmetric r matrices on hom lie algebras as particular cases of o operators on hom lie algebras

simple lie color algebras of witt type abstract let k be a field and let e k be a bicharacter defined on the multiplicative group we suppose that a is a graded associative k algebra that is color commutative with respect to e furthermore let be a nonzero graded k vector space of color derivations of a and suppose that is also color commutative with respect to the bicharacter e then with a rather natural definition a k a becomes a lie color algebra and we obtain necessary and sufficient conditions here for this lie color algebra to be simple with two minor exceptions when dim k 1 simplicity occurs if and only if a is graded simple and a a acts faithfully as color derivations on a

cohomology of lie superalgebras and their generalizations the cohomology groups of lie superalgebras and more generally of e lie algebras are introduced and investigated the main emphasis is on the case where the module of coefficients is nontrivial two general propositions are proved which help to calculate the cohomology groups several examples are included to show the peculiarities of the super case for l sl 1 2 the cohomology groups h1 l v and h2 l v with v a finite dimensional simple graded l module are determined and the result is used to show that h2 l u l with u l the enveloping algebra of l is trivial this implies that the superalgebra u l does not admit any nontrivial formal deformations in the sense of gerstenhaber garland s theory of universal central extensions of lie algebras is generalized to the case of e lie algebras

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

zeta values and differential operators on the circle abstract the fock representation of the virasoro lie algebra is extended to a larger graded lie subalgebra of the algebra of differential operators on the circle the central cocycle is related to values of the riemann zeta function at odd negative integers the corresponding generating function is related to eisenstein series for sl 2 z an analogous result is obtained for values of l series associated to even dirichlet characters using differential operators of infinite order

two parameter deformation of virasoro algebra in this paper the two parameter deformation of virasoro algebra is derived two parameter deformation of central charge is also obtained the operator product expansion for p q deformed virasoro algebra is derived

construction of n lie algebras and n ary hom nambu lie algebras as n ary operations generalizing lie and poisson algebras arise in many different physical contexts it is interesting to study general ways of constructing explicit realizations of such multilinear structures generically they describe the dynamics of a physical system and there is a need of understanding their quantization hom nambu lie algebras provide a framework that might be an appropriate setting in which n lie algebras n ary nambu lie algebras can be deformed and their quantization studied we present a procedure to construct n 1 ary hom nambu lie algebras from n ary hom nambu lie algebras equipped with a generalized trace function it turns out that the implications of the compatibility conditions that are necessary for this construction can be understood in terms of the kernel of the trace function and the range of the twisting maps furthermore we investigate the possibility of defining n k lie algebras from n lie algebras and a k form satisfying certain conditions

hom gel fand dorfman bialgebras and hom lie conformal algebras the aim of this paper is to introduce the notions of hom gel fand dorfman bialgebra and hom lie conformal algebra in this paper we give four constructions of hom gel fand dorfman bialgebras also we provide a general construction of hom lie conformal algebras from hom lie algebras finally we prove that a hom gel fand dorfman bialgebra is equivalent to a hom lie conformal algebra of degree 2

bihom novikov algebras and infinitesimal bihom bialgebras abstract we introduce and study infinitesimal bihom bialgebras bihom novikov algebras bihom novikov poisson algebras and find some relations among these concepts our main result is to show how to obtain a left bihom pre lie algebra from an infinitesimal bihom bialgebra

extensions and contractions of the lie algebra ofq pseudodifferential symbols on the circle abstract we construct cocycles on the lie algebra of pseudo and q pseudodifferential symbols of one variable and on their close relatives the sine algebra and the poisson algebra on two torus a quantum godbillon vey cocycle on pseudo differential operators appears in this construction as a natural generalization of the gelfand fuchs 3 cocycle on periodic vector fields a nontrivial embedding of the virasoro algebra into a completion of q pseudodifferential symbols is proposed we describe q analogs of the kp and kdv hierarchies admitting an infinite number of conserved charges as well as q deformed gelfand dickey structures

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

hom hopf group coalgebras and braided t categories obtained from hom hopf algebras the main aim of this paper is to provide new examples of braided t categories in the sense of turaev arabian j sci eng sect c 33 2c 483 503 2008 for this purpose we first introduce a class of new twisted yetter drinfeld modules categories then we construct a new braided t category generalizing the main constructions by panaite and staic isr j math 158 349 366 2007 finally we show that the new braided t category in some conditions coincides with the representations of a certain hom hopf group coalgebra that we construct

minimal unitary models and the closed invariant spin chain we consider the hamiltonian of the closed invariant chain we project a particular class of statistical models belonging to the unitary minimal series a particular model corresponds to a particular value of the coupling constant the operator content is derived this class of models has charge dependent boundary conditions in simple cases ising three state potts corresponding hamiltonians are constructed these are non local as the original spin chain

the category of yetter drinfel d hom modules and the quantum hom yang baxter equation in this paper we introduce the category of yetter drinfel d hom modules which is a braided monoidal category and show that the category of yetter drinfel d hom modules is a full monoidal subcategory of the left center of left hom module category also we study the equivalent relationship between the category of yetter drinfel d hom modules and the category of hom modules over the drinfel d double finally the faddeev reshetikhin takhtajan frt type theorem for the quantum hom yang baxter equation is investigated

hom novikov algebras we study a twisted generalization of novikov algebras called hom novikov algebras in which the two defining identities are twisted by a linear map it is shown that hom novikov algebras can be obtained from novikov algebras by twisting along any algebra endomorphism all algebra endomorphisms on complex novikov algebras of dimensions 2 or 3 are computed and their associated hom novikov algebras are described explicitly another class of hom novikov algebras is constructed from hom commutative algebras together with a derivation generalizing a construction due to dorfman and gel fand two other classes of hom novikov algebras are constructed from hom lie algebras together with a suitable linear endomorphism generalizing a construction due to bai and meng

a hom version of the affinizations of balinskii novikov and novikov superalgebras in this paper we introduce the notions of hom balinskii novikov and hom novikov superalgebras in which the defining identities are twisted by homomorphisms then we construct some infinite dimensional hom lie superalgebras by the affinizations of the above two hom superalgebras moreover we apply the bilinear forms with some invariance conditions on the hom balinskii novikov and hom novikov superalgebras to construct central extensions of the infinite dimensional hom lie superalgebras

cyclic homology of differential operators the virasoro algebra and a q analogue we show how methods from cyclic homology give easily an explicit 2 cocycle on the lie algebra of differential operators of the circle such that restricts to the cocycle defining the virasoro algebra the same methods yield also aq analogue of as well as an infinite family of linearly independent cocycles arising when the complex parameterq is a root of unity we use an algebra ofq difference operators andq analogues of koszul and the rham complexes to construct these quantum cocycles

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

generalization of h pseudoalgebraic structures the goal of this paper is to study hom h pseudoalgebraic structures generalizing h pseudoalgebras of associative and lie type we provide examples of the new structures and present some properties and construction theorems similar to the case of h pseudoalgebras the annihilator algebras are also discussed we also describe the equivalent definitions of hom h pseudoalgebra finally we consider the cohomology theory of hom h pseudoalgebra with coefficients in an arbitrary module furthermore the connection between the cohomology of hom lie h pseudoalgebra and its corresponding annihilator algebra is depicted

quasi lie structure of σ derivations of c t 1 hartwig larsson and silvestrov in j t hartwig d larsson s d silvestrov deformations of lie algebras using derivations j algebra 295 2 2006 314 361 defined a bracket on derivations of a commutative algebra we show that this bracket preserves inner derivations and based on this obtain structural results providing new insights into derivations on laurent polynomials in one variable