Matej Brešar

On the distance of the composition of two derivations to the generalized derivations

A well-known theorem of E. Posner [10] states that if the composition d 1 d 2 of derivations d 1 d 2 of a prime ring A of characteristic not 2 is a derivation, then either d 1 = 0 or d 2 = 0. A number of authors have generalized this theorem in several ways (see e.g. [1], [2], and [5], where further references can be found). Under stronger assumptions when A is the algebra of all bounded linear operators on a Banach space (resp. Hilbert space), Posners theorem was reproved in [3] (resp. [12]). Recently, M. Mathieu [8] extended Posners theorem to arbitrary C * -algebras.

Multiplication algebra and maps determined by zero products

Let A be a finite dimensional central simple algebra. By the Skolem–Noether theorem, every automorphism of A is inner. We will give a short proof of a somewhat more general result. The concept behind this proof is the fact that every linear map on A belongs to the multiplication algebra of A. As an application we will describe linear maps α, β : A → A such that α(x)β(y) = 0 whenever xy = 0.

Values of noncommutative polynomials, Lie SkewIdeals and tracial Nullstellensätze

A subspace of an algebra with involution is called a Lie skew-ideal if it is closed under Lie products with skew-symmetric elements. Lie skew-ideals are classified in central simple algebras with involution (there are eight of them for involutions of the first kind and four for involutions of the second kind) and this classification result is used to characterize noncommutative polynomials via their values in these algebras. As an application, we deduce that a polynomial is a sum of commutators and a polynomial identity of

Lie superautomorphisms on associative algebras

d\times d

Functional identities in one variable

matrices if and only if all of its values in the algebra of

A local-global principle for linear dependence of noncommutative polynomials

d\times d

A note on values of noncommutative polynomials

matrices have zero trace.

Jordan {g, h}-derivations on tensor products of algebras

We consider Lie superautomorphisms of prime associative superalgebras. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in question is 2 or 4.

On Lie and associative algebras containing inner derivations

Let

On Maps Determined by Zero Products

A