We study noncommutative disc algebras associated to the free product of discrete subsemigroups of R +. These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely innnite. The nonself-adjoint subalgebras determine the semigroup up to isomorphism. Moreover, we establish a dilation theorem for contractive representations of these semigroups which yields a ...

The uncovering of new structure on the Cuntz semigroup a C*-algebra stable rank one leads to several applications: we answer affirmatively, for class rank-one C*-algebras, conjecture by Blackadar and Handelman dimension functions, global Glimm halving problem, problem realizing functions cone 2-quasitraces as ranks elements. We also gain insights into comparability properties positive elements ...

Let M denote the multiplicative semigroup of all n-by-n matrices over a finite field F and K a commutative ring with an identity element in which the characteristic of F is a unit. It is proved here that the semigroup algebra K[M] is the direct sum of n + 1 algebras, namely, of one full matrix algebra over each of the group algebras K[GL(r, F)] with r = 0, 1, ..., n . The degree of the relevant...

Let n, r ∈ N. The affine Schur algebra S̃(n, r) (of type A) over a field K is defined to be the endomorphism algebra of certain tensor space over the extended affine Weyl group of type Ar−1. By the affine Schur–Weyl duality it is isomorphic to the image of the representation map of the U(ĝl n ) action on the tensor space when K is the field of complex numbers. We show that S̃(n, r) can be defined...

We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the cons...

Abstract. The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in which we have investigated a similar relation on inverse semigroups. We use a new concept of ”restricted” representations and study the restricted s...

We study semigroup C*-algebras of ax + b-semigroups over integral domains. The goal is to generalize several results about C*-algebras of ax + bsemigroups over rings of algebraic integers. We prove results concerning K-theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat ax+b-semigroups over a large class of integral domains containing al...

Abstract We give a new and conceptually straightforward proof of the well-known presentation for Temperley–Lieb algebra, via an alternative presentation. Our method involves twisted semigroup algebras, we make use two apparently submonoids monoid.