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We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples.…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
The research described in this note aims at solving the constructive membership problem for the class of quasisimple classical groups. Our algorithms are developed in the black-box group model; that is, they do not require specific…
Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…
The general ideal of this paper is to answer the following question: given a numerical property of commuting graphs, a class of semigroups $\mathcal{C}$ and $n\in\mathbb{N}$, is it possible to find a semigroup in $\mathcal{C}$ such that the…
We consider numerical semigroups associated with normal weighted homogeneous surface singularities with rational homology sphere links. We say that a semigroup is representable if it can be realized in this way. In this article, we study…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.
We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.
We characterize the simplicity of universal C$^*$-algebras arising from multispinal groups. Let $\mathcal{O}_{G_{\max}}$ be the universal C$^*$-algebra associated to a multispinal group $G$. We show that the invertibility of a matrix…
Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid…
We discuss representations of monogenic functions over very regular groups.
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
It is a survey of the results obtained by K. Glazek's and his co-workers. We restrict our attention to the problems of axiomatizations of n-ary groups, classes of n-ary groups, properties of skew elements and homomorphisms induced by skew…
We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras. Beginning with the most basic definitions and technical lemmas, we present several results of historical importance, such as Cuntz's theorem on the existence…
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…
We characterize relatively hyperbolic groups whose reduced $C^*$-algebra is simple as those, which have no non-trivial finite normal subgroups.
This paper contains a survey of recent developments in investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algebras along with some new results on the image of word maps on…
This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.