Representations of skew polynomial algebras

Irreducible representations of the Cuntz algebras arising from polynomial embeddings

For an embedding φ of the Cuntz algebra OM into ON , OM is identified with a subalgebra φ(OM) of ON . We construct irreducible representations of ON with continuous parameters by extending irreducible representations of OM . They are not unitarily equivalent to any generalized permutative representation, especially not to any permutative representation by Bratteli-Jorgensen and Davidson-Pitts. ...

Nilpotent Elements in Skew Polynomial Rings

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

Euler-Poincaré characteristic and polynomial representations of Iwahori-Hecke algebras

The Hecke algebras of type A „ admit faithful representations by symmetrization operators acting on polynomial rings. These operators are related to the geometry of flag manifolds and in particular to a generalized Euler-Poincare characteristic denned by Hirzebruch. They provide g-idempotents, togetherwith a simple way to describe the irreducible representations of the Hecke algebra. The link w...

On annihilator ideals in skew polynomial rings

This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...

Free skew Boolean algebras