In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C∗-algebras generated by “universal” row contractions associated with F+n , the free semigroup with n generators. This class of C ∗-algebras includes the Cuntz-Toeplitz algebra C∗(S1, . . . , Sn) (resp. C ∗(B1, . . . , Bn)) generated by the creation operators on the f...

These are notes for a lecture given at Ohio University on June 3, 2006. An important topic in commutative algebra is the Rees algebra of an ideal in a commutative ring. The Rees algebra encodes a lot of information about the ideal and corresponds geometrically to a blow-up. One can represent the Rees algebra as the quotient of a polynomial ring by an ideal. This ideal is generated by the defini...

An IP* set in a semigroup is one which must intersect the set of finite products from any specified sequence. (If the semigroup is noncommutative, one must specify the order of the products, resulting in “left” and “right” IP* sets.) If A is a subset of N with positive upper density, then the difference set A−A = {x ∈ N : there exists y ∈ A with x+ y ∈ A} is an IP* set in (N,+). Defining analog...

We introduce a misere quotient semigroup construction in impartial combinatorial game theory, and argue that it is the long-sought natural generalization of the normal-play Sprague-Grundy theory to misere play. Along the way, we illustrate how to use the theory to describe complete analyses of two wild taking and breaking games.

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of evenand oddreduced supermatrices are investigated on a par. They can be unified i...

Given a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recogn...

A Banach algebra is Arens-regular when all its continuous functionals are weakly almost periodic, in symbols A⁎=WAP(A). To identify the opposite behaviour, Granirer called a extremely non-Arens regular (enAr, for short) quotient A⁎/WAP(A) contains closed subspace that has A⁎ as quotient. In this paper we propose simplification and quantification of concept. We say r-enAr, with r≥1, there an iso...

The Abelian Sandpile Model is a diffusion process on graphs, studied, under various names, in statistical physics, theoretical computer science, and algebraic graph theory. The model takes a rooted directed multigraph X , the ambient space, in which the root is accessible from every vertex, and associates with it a commutative monoidM, a commutative semigroup S, and an abelian group G as follow...

Let Λ be some class of Abelian groups. We say that a group A ∈ is determined by its endomorphism semigroup E⋆(A) in if the isomorphism ≅ E⋆(B), where B Λ, implies B. describe split groups $$ {\mathcal{QD}}_{\mathrm{cd}} completely decomposable quotient divisible their semigroups .