We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra An. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a ∗-extendible representation σ. A ∗-extendible representation of An is regular if the absolutely continuous part coincides with the type L part. All known exa...

We define two deformations of the Full Transformation Semigroup algebra. One makes the algebra “as semisimple as possible”, while another leads to an eigenvalue result involving Schur functions. Preliminaries The Full Transformation Semigroup on n letters, denoted Tn, is the semigroup of all set maps w : [n] → [n], where [n] = {1, 2, . . . , n} and the multiplication is the usual composition. S...

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

the main purpose of this paper is to establish a relation between universality of certain p-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. in particular, we show that if we take p to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, the...

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

A Schmidt group is a non-nilpotent finite group in which each proper subgroup is nilpotent. Each Schmidt group G can be described by three parameters p, q and v, where p and q are different primes and v is a natural number, v ≥ 1. Denote by S the class of all Schmidt groups which have the same parameters p, q and v. It is shown in this paper that the class S can be characterized by the properti...

We demonstrate that the perforative phenomena shown to occur among simple amenable C∗-algebras by Villadsen and Toms can be realized within a dynamical framework. More specifically, we construct a minimal homeomorphism for which the K0 group of the crossed product fails to be weakly unperforated, and a minimal homeomorphism for which the crossed product has the same Elliott invariant as an AT-a...

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...

We consider a model for diffusive phase transitions, for instance, the component separation in a binary mixture. Our model is described by two functions, the absolutete temperature θ := θ(t, x) and the order parameter w := w(t, x), which are governed by a system of two nonlinear parabolic PDEs. The order parameter w is constrained to have double obstacles σ∗ ≤ w ≤ σ∗ (i.e., σ∗ and σ∗ are the th...