The results in this paper were motivated by the case when the inverse semigroup is the McAlister monoid MX on a set X. In [1] we considered some very large convolution algebras on MX , including some C ∗-algebras. Our main focus in [1] was deciding on the primitivity of the algebras, and one key tool was the use of generalized Rukolaine idempotents. To define these very large convolution algebr...

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

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...

In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F = F (x1, ..., xn) be a free algebra of some variety Θ of linear algebras over K freely generated by a set X = {x1, ..., xn}, EndF be the semigroup of endomorphisms of F , and Aut EndF be the group of automorphisms of the semigroup EndF ...

Let A be a finite dimensional Q-algebra and Γ ⊂ A a Z-order. We classify those A with the property that Z 6 →֒U(Γ). We call this last property the hyperbolic property. We apply this in the case that A = KS a semigroup algebra with K = Q or K = Q( √ −d). In particular, when KS is semi-simple and has no nilpotent elements, we prove that S is an inverse semigroup which is the disjoint union of Higm...

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. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier ...

We consider a version of the notion of F -inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Kr...

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...