Lie and Jordan Structure in Simple Γ− Regular Ring

On generalized left (alpha, beta)-derivations in rings

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

Simple Finite Jordan Pseudoalgebras⋆

We consider the structure of JordanH-pseudoalgebras which are linearly finitely generated over a Hopf algebra H . There are two cases under consideration: H = U(h) and H = U(h)#C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits–Kantor–Koecher construction for finite Jordan pseudoalgebras and des...

The second dual of strongly zero-product preserving maps

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...

Reversible Skew Laurent Polynomial Rings and Deformations of Poisson Automorphisms

A skew Laurent polynomial ring S = R[x;α] is reversible if it has a reversing automorphism, that is, an automorphism θ of period 2 that transposes x and x and restricts to an automorphism γ of R with γ = γ. We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent...

Lie and Jordan Structures in Simple, Associative Rings