Cancellative semigroup

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

Semigroup identities in the monoid of triangular tropical matrices

Abstract: We show that the submonoid of all n×n triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities

On regularity properties of nonsymmetric ornstein-uhlenbeck semigroup in LP spaces

Abstract: We study properties of the transition semigroup Rt corresponding to the Hilbert space valued nonsymmctric Ornstein-Uhlenheck process possessing an invariant measure μ Necessary and sufficient condition is given for Rtφ to be infinitely smooth in the direction of the Reproducing Kernel of μ for every bounded Borel φ. Estimates on the derivatives of Rtφ are obtained and the same estimates are obtained for the adjoint semigroup. We give also necessary and sufficient conditions for Rt to be an integral operator on LP (H,μ) extending earlier results by Da Prato-Zabczyk and Fuhrman. It is shown also that the integral kernel possesses strong integrability properties. The transition semigroup is also investigated in the scale of Sobolev spaces generalizing those of Malliavin calculus. The transition semigroup turns out to be strongly continuous in those spaces and compact if it is integral in LP (H,μ) Finally, an application to some parabolic PDE's on Hilbert space is given.

Boundary quotients of C*-algebras of right LCM semigroups

Abstract: We study C*-algebras associated to right LCM semigroups, that is, semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal. If $P$ is such a semigroup, its C*-algebra admits a natural boundary quotient $\mathcal{Q}(P)$. We show that $\mathcal{Q}(P)$ is isomorphic to the tight C*-algebra of a certain inverse semigroup associated to $P$, and thus is isomorphic to the C*-algebra of an \'etale groupoid. We use this to give conditions on $P$ which guarantee that $\mathcal{Q}(P)$ is simple and purely infinite, and give applications to self-similar groups and Zappa-Sz\'ep products of semigroups.

The perkins semigroup has co-np-complete term-equivalence problem

Abstract: A semigroup term is a finite word in the alphabet x1, x2,…. The length of a term p, denoted by |p|, is the number of variables in p, including multiplicities. The term-equivalence problem for a finite semigroup S has as an instance a pair of terms {p,q} with size |p| + |q| and asks whether p ≈ q is an identity over S. It is proved here that $\mathbf{B^1_2}$, the six-element Perkins semigroup, has co-NP-complete term-equivalence problem, a result which leads to the completion of the classification of he term-equivalence problems for monoid extensions of aperiodic Rees matrix semigroups. From the main result it follows that there exist finite semigroups with tractable term-equivalence problems but having subsemigroups and homomorphic images with co-NP-complete term-equivalence problems.