σ-centralizers of generalized matrix algebras

Centralizers of Iwahori-hecke Algebras

To date, integral bases for the centre of the Iwahori-Hecke algebra of a finite Coxeter group have relied on character theoretical results and the isomorphism between the Iwahori-Hecke algebra when semisimple and the group algebra of the finite Coxeter group. In this paper, we generalize the minimal basis approach of an earlier paper, to provide a way of describing and calculating elements of t...

σ-Derivations in Banach algebras

Lie Algebras with Abelian Centralizers

We classify all finite dimensional Lie algebras over an algebraically closed field of characteristic 0, whose nonzero elements have abelian centralizers. These algebras are either simple or solvable, where the only simple such Lie algebra is sl2. In the solvable case they are either abelian or a one-dimensional split extension of an abelian Lie algebra.

Centres and Centralizers of Iwahori-hecke Algebras

This thesis describes the minimal basis for the centre of an Iwahori-Hecke algebra. Defining the Iwahori-Hecke algebra H over Z[ξs]s∈S a subring of the traditional ring of definition we begin by defining positivity in H, and by describing a very simple basis for the centralizer of the subalgebra generated by the element corresponding to a single simple reflection of the Coxeter group. This basi...

On (σ, τ)-module extension Banach algebras

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.