Ganna Kudryavtseva

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.

On the semigroup of square matrices

We study the structure of nilpotent subsemigroups in the semigroup M(n, F) of all n x n matrices over a field IF with respect to the operation of the usual matrix multiplication. We describe the maximal subsemigroups among the nilpotent subsemigroups of a fixed nilpotency degree and classify them up to isomorphism. We also describe isolated and completely isolated subsemigroups and conjugated elements in M(n, F).

Combinatorial Gelfand models for some semigroups and

Inspired by the results of Adin, Postnikov and Roichman, 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 algebras of the symmetric inverse semigroup to a Gelfand model for the q -rook monoid algebra.

q

We construct a family of representations of an arbitrary variant Sa of a semigroup S, induced by a given representation of S, and investigate properties of such representations and their kernels.

-rook monoid algebras

We refine Funk’s description of the classifying space of an inverse semigroup by replacing his

The classifying space of an inverse semigroup

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ORDERED SEMIGROUPS, UPPER-TRIANGULAR REFLEXIVE RELATIONS AND SEMIGROUPS OF LANGUAGES

∗-semigroups by right generalized inverse