In this paper, we study an approximate biflatness of l 1 S , where id="M2"> is a Clifford semigroup. Indeed, show that semigroup algebra id="M3"> approximately biflat if and only every maximal subgroup id="M4"> amenable...

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...

A free semigroup algebra is the wot-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting features. The first is that they provide useful information about unitary invariants of representations of the Cuntz–Toeplitz algebras. The second is that they form a class of nonself-adjoint opera...

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S = k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We investigate when algebras of multiplicative invariants are semigroup algebras. In particular, we present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection...

A new construction of a free inverse semigroup was obtained by Poliakova and Schein in 2005. Based on their result, we find a Gröbner-Shirshov basis of a free inverse semigroup relative to the deg-lex order of words. In particular, we give the (unique and shortest) Gröbner-Shirshov normal forms in the classes of equivalent words of a free inverse semigroup together with the Gröbner-Shirshov alg...

‎we present a characterization of arens regular semigroup algebras‎ ‎$ell^1(s)$‎, ‎for a large class of semigroups‎. ‎mainly‎, ‎we show that‎ ‎if the set of idempotents of an inverse semigroup $s$ is finite‎, ‎then $ell^1(s)$ is arens regular if and only if $s$ is finite‎.

This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C∗algebras: (i) Jiang-Su stability, (ii) unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case that the C∗-algebra is approximately subhomogeneous). An example is given of a simple, separable, nuclear, stably projectionless C∗-algebra whos...

In recent years there has been a growing number of constructions of faithful irreducible representations for the semigroup algebra FS of some specific inverse semigroups S. As usual, when S has a zero element θ, the contracted semigroup algebra F0S = FS/Fθ is considered. When F = C, the interest has been on faithful irreducible ∗-representations of CS (or C0S), and also `(S) (or `0(S)), on an i...

This paper studies algebras of operators associated to a semigroup algebra. The ring of differential operators is shown to be anti-isomorphic to the symmetry algebra and both are described explicitly in terms of the semigroup. As an application, we produce a criterion to determine the equivalence of A-hypergeometric systems. Conditions under which associated algebras are finitely generated are ...

Denote by (R, ·) the multiplicative semigroup of an associative algebra R over an infinite field, and let (R, ◦) represent R when viewed as a semigroup via the circle operation x ◦ y = x + y + xy. In this paper we characterize the existence of an identity in these semigroups in terms of the Lie structure of R. Namely, we prove that the following conditions on R are equivalent: the semigroup (R,...