Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.

The Local Cohomology Groups of an Affine Semigroup Ring

Abstract: Publisher Summary This chapter provides an overview of the local cohomology groups of an affine semigroup ring. A commutative semigroup ring k [ S ] over a field k is said to be an affine semigroup ring if k [ S ] is an integral domain of finite type over k . This is equivalent to the condition that S is finitely generated and is contained in a free Z-module M of finite rank. An affine semigroup ring k [ S ] has a natural structure of an M-graded ring with respect to the free Z-module M. The dualizing complex and the local cohomology groups are also described in the chapter.

Normal semigroups of one-to-one transformations

Abstract: If a transformation semigroup S is defined by means of certain properties there is aproblem of determining the elements of S explicitly. In this paper, the above problem isconsidered for ^-normal semigroups S of total one-to-one transformations of a set X.A transformation semigroup S on X is termed ^-norma

Brownian motion on Lie groups and open quantum systems

Abstract: We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.

The left regular *-representation of an inverse semigroup

Abstract: The left regular *-representation of the semigroup algebra of an inverse semigroup is faithful. Clifford semigroups with a particular type of semilattice are shown to have the weak containment property if and only if each subgroup is amenable. An inverse semigroup is a semigroup in which for each element s there exists a unique element, which we denote s*, such that ss*s = s and s*ss* =s*. From this it follows that the idempotents commute, products of idempotents are idempotents, and (st)* = t*s* [5, pp. 130-131]. For an inverse semigroup S, Es will denote the set of idempotents of S. ES is a lower semilattice under the operation e A f = ef . A Clifford semigroup is an inverse semigroup T whose idempotents are central; then T = U{Ge: e E ET} where Ge is the greatest subgroup of T containing e. We identify s E S with the function in 11(S) which is 1 at s and 0 elsewhere. Then l1(S) is a Banach algebra with multiplication the continuous bilinear extension of the semigroup multiplication, called the (11-)semigroup algebra of S. The involution * on S extends to a unique continuous involution * on 11(S) by conjugate linearity. Then l(S) is a Banach star algebra. Barnes [1] constructed the left regular *-representation of l1(S) (on 12(S)), which we will denote by Ls, by Ls(a)b = { ab if a*ab = b, i.e. if a*a > bb*,