A classical theorem of Veldkamp describes the center an enveloping algebra a Lie semi-simple algebraic group in characteristic p . We generalize this result to class algebras with property that they arise as reduction modulo ≫ 0 from g , such has no nontrivial semi-invariants Sym ( ) and is polynomial algebra. As application, we solve derived isomorphism problem for above algebras.

The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and integrable systems. This paper gives a complete classification of PostLie algebra structures on the Lie algebra sl(2,C) up to isomorphism. The classificatio...

As Don Schack mentioned in his plenary talk [SDS], Gerstenhaber [MG] observed that if A is an associative algebra, then the Hochschild cohomology of A is a graded commutative algebra with an additional structure, viz., that of a Lie algebra. The two structures satisfy a compatibility condition (graded Poission structure). We agree to call such structures G–algebras (Gerstenhaber–algebras). Scha...

This article is part of a study on solvable Leibniz algebras with given nilradical. In this paper, algebras, whose nilradical naturally graded quasi-filiform algebra and the complemented space to has maximal dimension, are described up isomorphism.

Let τ be an invertible skew pairing on (B,H), where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HYD and there exists a Hopf algebra isomorphism w : B∞H → B τH in C, where B∞H is a Hopf algebra with (co)algebra structure the smash (c...

By Tits’ deformation argument, a generic Iwahori–Hecke algebra H associated to a finite Coxeter group W is abstractly isomorphic to the group algebra of W . Lusztig has shown how one can construct an explicit isomorphism, provided that the Kazhdan–Lusztig basis of H satisfies certain deep properties. If W is crystallographic and H is a one-parameter algebra, then these properties are known to h...

This paper introduces the concept of subalgebra and discusses some properties subalgebra. We also examine different types ideals how they behave. describe a homomorphism. Finally, we present quotient algebra discuss isomorphism theorems.

A differential Azumaya algebra, and in particular a differential matrix algebra, over a differential field K with constants C is trivialized by a Picard–Vessiot (differential Galois) extension E. This yields a bijection between isomorphism classes of differential algebras and Picard–Vessiot cocycles Z(G(E/K), PGLn(C)) which cobound in Z (G(E/K), PGLn(E)).

5. Commutation of left and right actions 97 5.1. Right g-modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.2. Opposite algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.3. Analogues of results on Lie algebra actions . . . . . . . . . . . . . . 104 5.4. A theorem connecting left and right actions . . . . . . . . . . . . . . 107 5.5. The right Guin-Ou...

To any germ X of a complex analytic variety with local ring OX one associates the topological Lie algebra Θ(X) = DerOX of vector fields on X. We show that isolated hypersurface singularities X of dimension at least 3 are uniquely determined up to isomorphism by the topological Lie algebra Θ(X).