some lie algebra analogues of schur's theorem and its converses are presented. as a result, it is shown that for a capable lie algebra l we always have dim l=z(l)  2(dim(l2))2. we also give give some examples sup- porting our results.

Based on the structure of Casimir elements associated with general Hopf algebras there are constructed Liouville-Arnold integrable flows related with naturally induced Poisson structures on arbitrary co-algebra and their deformations. Some interesting special cases including the oscillatory Heisenberg-Weil algebra related co-algebra structures and adjoint with them integrable Hamiltonian system...

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...

We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

and Applied Analysis 3 Park and Rassias 59 proved the stability of homomorphisms in C∗-algebras and Lie C∗-algebras and also of derivations on C∗-algebras and Lie C∗-algebras for the Jensen-type functional equation μf ( x y 2 ) μf ( x − y 2 ) − fμx 0 1.6 for all μ ∈ T1 : {λ ∈ C; |λ| 1}. In this paper, by using the fixed-point methods, we establish the stability of n-Lie homomorphisms and Jordan...

1. Lie groups, homomorphisms and linear representations. Irreducible representations. 2. Maximal tori in compact Lie groups. 3. Characters of representations. Ring of virtual characters. The Weyl theorem. 4. Actions of Lie groups. Homogeneous spaces (orbits) and equivariant maps. 5. Classifying spaces of topological groups and maps induced by homomorphisms. 6. Homotopy classification of maps be...