Related papers: Remarks to Glazek's results on n-ary groups

We survey results related to the important Hossz\'u-Gluskin Theorem on $n$-ary groups adding also several new results and comments. The aim of this paper is to write all such results in uniform and compressive forms. Therefore some proofs…

The book "N-ary Groups" (in Russian) consists of two Parts. It is intended on the one hand as an initial introduction to the theory of n-ary groups, and on the other hand it contains the published results by the author on this subject. At…

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the…

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.

The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.

This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer…

The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik's double affine Hecke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin…

We compute the group homology, the algebraic $K$- and $L$-groups, and the topological $K$-groups of right-angled Artin groups, right-angled Coxeter groups, and more generally, graph products.

Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Brou\'e-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for…

This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…

For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.

We survey some recent work on the geometric Satake of p-adic groups and its applications to some arithmetic problems of Shimura varieties. We reformulate a few constructions appeared in the previous works more conceptually.

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…

This survey article, is written as an extended note and supplement of my lectures in the current developments in mathematics conference in 2015. We discuss some recent developments on the conjugacy classes of affine Weyl groups and $p$-adic…

The aim of this paper is two fold: First to study finite groups $G$ of automorphisms of the homogenized Weyl algebra $B_{n}$, the skew group algebra $B_{n}\ast G$, the ring of invariants $B_{n}^{G}$, and the relations of these algebras with…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.

In this expository paper we review some recent results about representations of Kac-Moody groups. We sketch the construction of these groups. If practical, we present the ideas behind the proofs of theorems. At the end we pose open…

We investigate monotone idempotent $n$-ary semigroups. One of the main result of this article is the generalisation of Czogala-Drewniak Theorem, which describes the idempotent monotone associative functions having neutral element.…

A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.