Related papers: Finite and semisimple Boolean inverse monoids

It was proved by Oliveira and Silva (2005) that every finitely generated inverse subsemigroup of the monogenic free inverse semigroup $FI_1$ is finitely presented. The present paper continues this development, and gives generating sets and…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…

Finite-above inverse monoids are a common generalization of finite inverse monoids and Margolis--Meakin expansions of groups. Given a finite-above $E$-unitary inverse monoid $M$ and a group variety $\mathit{U}$, we find a condition for $M$…

We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.

We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…

This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.

The authors [3] proved that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and described its monolith. Here we prove that the endomorphism semiring of a commutative inverse semigroup with at least…

The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all…

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…

We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…

We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups, called Boolean inverse $\wedge$-semigroups, with a class of topological groupoids, called Hausdorff Boolean groupoids. Much of the paper…

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

This thesis addresses questions in representation and invariant theory of finite groups. The first concerns singularities of quotient spaces under actions of finite groups. We introduce a class of finite groups such that the quotients have…

The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…

In the paper we study (countably) compact and (absolutely) $H$-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably…

We present a general method for proving that a semigroup is non-finitely based. The method is strong enough to cover the non-finite basis arguments in articles [1,3,4,5,7,8, 11,14,16,21,27,31,36,37]. In particular, the method allows to…

We introduce $X$-to-join representations of inverse semigroups which are a relaxation of the notion of a cover-to-join representation. We construct the universal $X$-to-join Booleanization of an inverse semigroup $S$ as a weakly…

In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is…

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.