the frechet and limiting subdifferentials of integral functionals on the spaces l1 ω e abstract a new approach to computing the frechet subdifferential and the limiting subdifferential of integral functionals is proposed thanks to this way we obtain formulae for computing the frechet and limiting subdifferentials of the integral functional f u f u d u l 1 e here a is a measured space with an atomless finite complete positive measure e is a separable banach space and f e r under some assumptions it turns out that these subdifferentials coincide with the fenchel subdifferential of f

composition algebras with large derivation algebras abstract the finite dimensional flexible composition algebras include the hurwitz algebras composition algebras with unit element but also other interesting classes of algebras the para hurwitz and the okubo algebras the above mentioned algebras present many symmetries and this is reflected in their large derivation algebras in the present paper we study the opposite question what can be said about the composition algebras if we have some information about their derivation algebras our main result is the classification of all the composition algebras with such large derivation algebras

on lie gradings ii abstract to obtain fine gradings of gl n c it is necessary to study maximal abelian subgroups mad subgroups of diagonizable automorphisms in a ut gl n c we described two finite sets h n and k n such that each mad subgroup consisting only from inner automorphisms is conjugated to some element of h n and each mad subgroup containing at least one outer automorphism is conjugated to some element of k n using these results concerning k n we then easily find all mad subgroups in a ut o n c for n 8 and in a ut sp 2n c

on triality and automorphisms and derivations of composition algebras abstract the principle of triality for orthogonal transformations on eight dimensional spaces is used to obtain different expressions for the automorphisms derivations and orthogonal transformations of cayley dickson algebras and symmetric composition algebras over fields of arbitrary characteristic

a lie grading which is not a semigroup grading this note is devoted to the construction of a graded lie algebra whose grading is not given by a semigroup thus providing a counterexample to an assertion by patera and zassenhaus

limiting subdifferentials of indefinite integrals abstract we compute the limiting subdifferential f x of the indefinite integral of the form f x a x f t d t where f is an essentially bounded measurable function or a function continuous on an interval containing x r except for possibly x or a step function which has a countable number of steps around x the related problem of computing the aumann integral of the limiting subdifferential mapping f where f is a lipschitz real function defined on an open set u r n is also investigated

special and pure gradings of lie algebras 136 w h hesselink m f p since h is strict the mapf is uniquely determined by the gradings h and h conversely the grading h is determined by h and f if n is a subgroup of m and m m n and f is the quotient map then h is called the quotient grading h h n see 2 8 for an example strict gradings h and are called equivalent if they dominate each other they are called conjugate if there is an automorphism g of l such that h is equivalent to the grading gh ghm m m the automorphism group a h of a strict grading h of l is defined to consist of the automorphisms g of l such that gh is equivalent to h let a h be the image of a h in the automor phism group gl m of m in 3 9 we prove proposition a a h is a finite group b let l be semisimple then a h is finite if and only if h is special 1 4 let l be a semisimple lie algebra over k of rank 1 if h is a pure grading of l its graduation group m is an lf2 space of rank r with 1 r 1 cf 4 1 assume that l has a split caftan subalgebra c let cg l be the root space decomposition of l let 9 be the root system and let q be the lattice spanned by 9 in the dual c of c let w be the weyl group a grading h is called c pure if cch with s 0 since 2s 0 we have the quotient grading h h o s with the graduation group m m o s as c cho there is a unique homomorphism f q m such that l h i if a b since h is strict f is surjective the kernel of f is called the com plementary lattice e of h since m is an ifz space we have 2qce conversely we have

on some algebras related to simple lie triple systems abstract the set hom der t t f t t is determined for any simple finite dimensional lie triple system t over a field f of characteristic zero it turns out that it contains nontrivial elements if and only if t is related to a simple jordan algebra in particular this provides a new proof of the determination by laquer of the invariant affine connections in the simply connected compact irreducible riemannian symmetric spaces

on the completeness of photon added coherent states we demonstrate explicitly the completeness of photon added coherent states pacss introduced by agarwal and tara agarwal g s and tara k 1991 phys rev a 43 492 and defined up to normalization by m z m 0 1 2 where is the boson creation operator and z are conventional glauber klauder coherent states we find the analytical form of the positive weight function in their resolution of unity by solving the associated stieltjes power moment problem we furnish an example of generation of another set of pacss which are complete

models of the octonions and g2 different models of the cayley algebras and of their lie algebras of derivations are given based on some distinguished subalgebras of the later ones

nonclassical properties of coherent states and excited coherent states for continuous spectra based on the definition of coherent states for continuous spectra and analogous to photon added coherent states for discrete spectra we introduce the excited coherent states for continuous spectra it is shown that the main axioms of gazeau klauder coherent states will be satisfied properly nonclassical properties and quantum statistics of coherent states as well as the introduced excited coherent states are discussed in particular through the study of quadrature squeezing and amplitude squared squeezing it will be observed that both classes of the above states can be classified in the intelligent states category

gradings on symmetric composition algebras abstract the group gradings on the symmetric composition algebras over arbitrary fields are classified applications of this result to gradings on the exceptional simple lie algebras are considered too

division composition algebras through their derivation algebras abstract composition algebras are algebras with a nondegenerate quadratic multiplicative form in this paper we construct five families of division composition algebras and prove that any division composition algebra with nonabelian derivation algebra belongs to one of these families as a by product we obtain new examples of real division algebras

composition algebras satisfying certain identities abstract even though the class of power associative algebras is huge only hurwitz algebras appear in the case of composition algebras not necessarily unital over fields of characteristic different from two under this assumption and other conditions weaker than power associativity we study in this note composition algebras of arbitrary dimension first a characterization of hurwitz algebras is given when the ground field has at least five elements more cases are considered so by using conditions on powers of every element we characterize when a composition algebra over a field of characteristic different from 2 and 3 and with at least 7 elements is hurwitz or its norm is associative similar characterizations are given for composition algebras that are hurwitz or standard ii respectively hurwitz or standard iii

real division algebras with large automorphism group we continue the study of the 8 dimensional real division algebras whose derivation algebra is large of type g2 a2 2a1 or a1 begun by benkart and osborn in the early 1980s for some of the families of real algebras that they constructed we find necessary and sufficient conditions for them to be division algebras determine when two division algebras in such a family are isomorphic or determine the automorphism group of such an algebra we use one of these families to prove that every 2 dimensional real division algebra embeds in a 4 dimensional and in an 8 dimensional real division algebra a new family f6 of non isomorphic real 8 dimensional algebras parametrized by the euclidean space r6 is constructed and studied in detail the division algebras in f6 correspond to a non empty open subset of the parameter space we also introduce an interesting 2 parameter subfamily f2 f6 which contains the generalized pseudo octonion algebras we obtain necessary and sufficient conditions for a f2 to be a division algebra in the generic case the algebras in f6 are 1 generated and have so 3 as the automorphism group we also determine all 1 2 and 4 dimensional subalgebras of the division algebras in f6 we show that there exist 8 dimensional and 4 dimensional real division algebras having a 1 dimensional subalgebra not contained in any 2 dimensional subalgebra we also construct 8 dimensional real division algebras having a 2 dimensional subalgebra not contained in any 4 dimensional subalgebra

symmetric composition algebras abstract a construction of all the okubo algebras over fields of characteristic 3 is provided and the complete classification of the composition algebras with associative norm over fields is finished

gradings on simple jordan and lie algebras abstract in this paper we describe all group gradings by a finite abelian group g of several types of simple jordan and lie algebras over an algebraically closed field f of characteristic zero

coherent states for systems with discrete and continuous spectrum for a system with one degree of freedom coherent states that are parametrized by classical canonical action angle variables are introduced these states also possess continuity of labelling a resolution of unity and temporal stability the insistence on canonical action angle variables strongly restricts any remaining arbitrariness in the coherent state definition such states are introduced for semibounded hamiltonian operators having either a discrete or a continuous spectrum hamiltonians that have both discrete and continuous parts in their spectrum are also discussed

the construction of some important classes of generalized coherent states the nonlinear coherent states method considering some important classes of generalized coherent states known in the literature we demonstrated that all of them can be created via conventional methods i e the lowering operator eigenstate and the displacement operator techniques using the nonlinear coherent states approach as a result we obtained a unified method to construct a large class of coherent states which have already been introduced by different prescriptions

color algebras and affine connections on s6 the classification of algebras having a given lie group as their automorphism group has recently surged as an important problem in the study of general structure theory of algebras particle physics differential geometry and invariant system theory 2 4 11 14 17 191 since the automorphism group aut a of a real or complex algebra a is a lie group whose lie algebra is the derivation algebra der a of a zl 1 this is equivalent to the problem of classifying algebras having a given lie algebra as their derivation algebra symmetries that frequently appear in physics are represented by automorphisms of certain nonassociative algebras a where the largeness of aut a or der a reflects the symmetries such algebras with the symmetry group x 3 c su 3 or the compact exceptional lie group g2 have extensively been investigated in particle physics geometry of affrne connections on a reductive homogeneous space and for the study of nite dimensional real division algebras z 4 14 191 the color algebra of domokos and kiivesi domokos 4 o onion and para octonion algebras and the complex or real okubo algebra s are examples of such algebras a well known theorem of f adams asserts that if the sphere s admits

classification of the finite dimensional real division composition algebras having a non abelian derivation algebra we classify the category of finite dimensional real division composition algebras having a non abelian lie algebra of derivations our complete and explicit classification is largely achieved by introducing the concept of a quasi description of a category and using it to express the problem in terms of normal form problems for certain group actions on products of 3 spheres

second order subdifferentials and convexity of real valued functions abstract in this paper we show that the positive semi definiteness psd of the frechet and or mordukhovich second order subdifferentials can recognize the convexity of c 1 functions however the psd is insufficient for ensuring the convexity of a locally lipschitz function in general a complete characterization of strong convexity via the second order subdifferentials is also given