Algebras of Jordan brackets and generalized Poisson algebras

Generalized Witt Algebras and Generalized Poisson Algebras

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra [1],[3],[13]. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra [13]. We also generalize the Hamitonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.

Hom-alternative Algebras and Hom-jordan Algebras

The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra. INTRODUCTION Hom-algebraic structures are algebras where the identities defining the st...

Jordan Derivations and Antiderivations of Generalized Matrix Algebras

Let G = [ A M N B ] be a generalized matrix algebra defined by the Morita context (A,B,A MB,B NA,ΦMN ,ΨNM) . In this article we mainly study the question of whether there exist the so-called “proper” Jordan derivations for the generalized matrix algebra G . It is shown that if one of the bilinear pairings ΦMN and ΨNM is nondegenerate, then every antiderivation of G is zero. Furthermore, if the ...

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras