Let Γ be an infinite discrete group and βΓ its Čech-Stone compactification. Using the well known fact that a free ultrafilter on an infinite set is nonmeasurable, we show that for each element p of the remainder βΓ \ Γ, left multiplication Lp : βΓ → βΓ is not Borel measurable. Next assume that Γ is abelian. Let D ⊂ l(Γ) denote the subalgebra of distal functions on Γ and let D = Γ = |D| denote t...

This paper is a contribution to the theory of what might be termed $0$-dimensional non-commutative spaces. We prove that associated with each inverse semigroup $S$ Boolean presented by abstract versions Cuntz-Krieger relations. call this Exel completion and show it arises from Exel's tight groupoid under Stone duality.

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

We survey some connections between topological dynamics, semigroups of ultrafilters, and combinatorics. As an application, we give a proof, based on ideas of Bergelson and Hindman, of the Hales-Jewett partition theorem. Furstenberg and his co-workers have shown [15, 16, 17] how to deduce combinatorial consequences from theorems about topological dynamics in compact metric spaces. Bergelson and ...

We define a class of transversal slices in spaces which are quasi-Poisson for the action complex semisimple group G. This is multiplicative analogue Whittaker reduction. One example universal centralizer Z G, equipped with usual symplectic structure this way. construct smooth relative compactification Z‾ by taking closure each fiber wonderful By realizing as larger variety, we show that it and ...

We introduce a new class of noncommutative rings-Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Galois orders generalizes classical orders in noncommutative rings and contains many classical objects, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, assoc...

The traditional approach to fault-tolerant computation has been via modular redundancy. Although universal and simple, modular redundancy is inherently expensive and inefficient. By exploiting particular structural features of a computation or algorithm, recently developed Algorithm-Based Fault Tolerance (ABFT) techniques manage to offer more efficient fault coverage at the cost of narrower app...

The concept of an automatic structure has been generalized from groups [ECH+] to semigroups [CRRT]. Several authors [CRR, Hof, Kam] have asked the following question: Let S be a finitely generated semigroup embeddable in a group and let G be its universal group [CP, Chapter ]. If G is automatic, must S be automatic? Examples in favour of this implication include: free groups and s...

This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B2, denoted V(B2). We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by B2 which leads to the main result, which states that V(B2) is decidable. Independently, using some suggestions given by J. Almeida in his book “Finite Semigroups an...