A presentation for the partial dual inverse symmetric monoid
We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid.
math.GR↗
arXiv subjects
Ganna Kudryavtseva
Publications and source records attributed to Ganna Kudryavtseva.
On conjugacy in regular epigroups
Let $S$ be a semigroup. The elements $a,b\in S$ are called primarily conjugate if $a=xy$ and $b=yx$ for certain $x,y\in S$. The relation of conjugacy is defined as the transitive closure of the relation of primary conjugacy. In the case when $S$ is a monoid, denote by $G$ the group of units of $S$. Then the relation of $G$-conjugacy is defined by $a\sim_G b \iff a=g^{-1}bg$ for certain $g\in G$. We establish the structure of conjugacy classes for regular epigroups (i.e. semigroups such that some power of each element lies in a subgroup). As a corollary we obtain a criterion of conjugacy in terms of $G$-conjugacy for factorizable inverse epigroups. We show that our general conjugacy criteria easily lead to known and new conjugacy criteria for some specific semigroups, among which are the full transformation semigroup and the full inverse symmetric semigroup over a finite set, the linear analogues of these semigroups and the semigroup of finitary partial automatic transformations over a finite alphabet.
math.GR↗
On presentations of Brauer-type monoids
We obtain presentations for the Brauer monoid, the partial analogue of the Brauer monoid, and for the greatest factorizable inverse submonoid of the dual symmetric inverse monoid. In all three cases we apply the same approach, based on the realization of all these monoids as Brauer-type monoids.
math.GR↗
The structure of automorphism groups of semigroup inflations
It is proved that the automorphism group of a semigroup being an inflation of its proper subsemigroup decomposes into a semidirect product of two groups one of which is a direct sum of full symmetric groups.
math.GR↗
On representations of variants of semigroups
We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.
math.GR↗
On Kiselman's semigroup
We study the algebraic properties of the series $\mathrm{K}_n$ of semigroups, which is inspired by \cite{Ki} and has origins in convexity theory. In particular, we describe Green's relations on $\mathrm{K}_n$, prove that there exists a faithful representation of $\mathrm{K}_n$ by $n\times n$ matrices with non-negative integer coefficients (and even explicitly construct such a representation), and prove that $\mathrm{K}_n$ does not admit a faithful representation by matrices of smaller size. We also describe the maximal nilpotent subsemigroups in $\mathrm{K}_n$, all isolated and completely isolated subsemigroups, all automorphisms and anti-automorphisms of $\mathrm{K}_n$. Finally, we explicitly construct all irreducible representations of $\mathrm{K}_n$ over any field and describe primitive idempotents in the semigroup algebra (which we prove is basic).
math.GR↗
$\mathcal{L}$-- and $\mathcal{R}$--cross-sections in the Brauer semigoup
We classify all cross-sections of Green's relations $\mathcal{L}$ and $\mathcal{R}$ in the Brauer semigroup. The regular behavior of such cross-sections starts from $n=7$. We show that in the regular case there are essentially two different cross-sections and all others are $\mathcal{S}_n$-conjugated to one of these two. We also classify all cross-sections up to isomorphism.
math.GR↗