Related papers: A semigroup theoretic approach to Whitehead's asph…
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
We develop a theory of adjunctions in semigroup categories, i.e. monoidal categories without a unit object. We show that a rigid semigroup category is promonoidal, and thus one can naturally adjoin a unit object to it. This extends the…
An interesting question about quasiconvexity in a hyperbolic group concerns finding classes of quasiconvex subsets that are closed under finite intersections. A known example is the class of all quasiconvex subgroups. However, not much is…
In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial…
We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial…
The concept of asphericity for relative group presentations was introduced twenty five years ago. Since then, the subject has advanced and detailed asphericity classifications have been obtained for various families of one-relator relative…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by…
We give a criterion of the semisimplicity of a p-adic unitary representation of a topological monoid by the reduction of the associated operator algebra.
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
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…
The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic…
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
We consider a family of cyclic presentations and show that, subject to certain conditions on the defining parameters, they are spines of closed 3-manifolds. These are new examples where the reduced Whitehead graphs are of the same type as…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which seem to be necessary to make the…
In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…