Fiat categorification of the symmetric inverse semigroup and the semigroup
نویسنده
چکیده
Starting from the symmetric group Sn , we construct two fiat 2-categories. One of them can be viewed as the fiat “extension” of the natural 2-category associated with the symmetric inverse semigroup (considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the symmetric inverse semigroup. The other 2-category can be viewed as the fiat “extension” of the 2-category associated with the maximal factorizable subsemigroup of the dual symmetric inverse semigroup (again, considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the maximal factorizable subsemigroup of the dual symmetric inverse semigroup.
منابع مشابه
Module cohomology group of inverse semigroup algebras
Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...
متن کاملArens regularity of inverse semigroup algebras
We present a characterization of Arens regular semigroup algebras $ell^1(S)$, for a large class of semigroups. Mainly, we show that if the set of idempotents of an inverse semigroup $S$ is finite, then $ell^1(S)$ is Arens regular if and only if $S$ is finite.
متن کاملCombinatorial Gelfand models for some semigroups and q-rook monoid algebras
Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...
متن کاملBrandt extensions and primitive topologically periodic inverse topological semigroups
In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...
متن کامل2n-Weak module amenability of semigroup algebras
Let $S$ be an inverse semigroup with the set of idempotents $E$. We prove that the semigroup algebra $ell^{1}(S)$ is always $2n$-weakly module amenable as an $ell^{1}(E)$-module, for any $nin mathbb{N}$, where $E$ acts on $S$ trivially from the left and by multiplication from the right. Our proof is based on a common fixed point property for semigroups.
متن کامل