Related papers: Primer on inverse semigroups II
A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$ if every element in $Q$ can be written as $a^{-1}b$ where $a,b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory. If we insist on $a$…
In [Trace identities and $\bf {Z}/2\bf {Z}$-graded invariants, {\it Trans. Amer. Math. Soc. \bf309} (1988), 581--589] we generalized the first and second fundamental theorems of invariant theory from the general linear group to the general…
We prove that four different notions of Morita equivalence for inverse semigroups motivated by, respectively, $C^{\ast}$-algebra theory, topos theory, semigroup theory and the theory of ordered groupoids are equivalent. We also show that…
We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial…
We show that in any infinitely distributive inverse semigroup the existing binary meets distribute over all the joins that exist.
Let $R$ be a ring with involution. The recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary $*$-ring case. It is shown that the group, Moore-Penrose, core and dual core inverse are closely…
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
In a group $G$, elements $a$ and $b$ are conjugate if there exists $g\in G$ such that $g^{-1} ag=b$. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse semigroups: for…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure.
This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
There are many examples of `binary' partial groups in the literature: sets equipped an identity and a partially-defined binary operation, such that each element admits an inverse. We show that many of these may be regarded as partial groups…
In this (partly expository) paper we show, using ideas from the theory of total positivity, how a number of properties of a semisimple group over the complex numbers can be presented purely in terms of the Weyl group. We also describe some…
Rejoinder to ``Microarrays, Empirical Bayes and the Two-Groups Model'' [arXiv:0808.0572]
We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.
The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…