Related papers: Linear quasigroups. I
The article is a continuation of the author's work "Linear quasigroups. I" and devoted to linear quasigroups and some of their generalizations. In the second part identities and linearity of quasigroups are investigated, in particular, the…
We present an overview of the theory of self-distributive quasigroups, both in the two-sided and one-sided cases, and relate the older results to the modern theory of quandles, to which self-distributive quasigroups are a special case. Most…
The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
The class of all quasigroups is covered by six classes: the class of all asymmetric quasigroups and five varieties of quasigroups (commutative, left symmetric, right symmetric, semi-symmetric and totally symmetric). Each of these classes is…
Quasigroup equational definitions are given.
We give an overview of various prolongations of quasigroups. Two step prolongation procedure is proposed.
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
\noindent 1. Generalities\hfil\break 2. Lie groups and Lie algebras\hfil\break 3. The unitary groups\hfil\break 4. Representations of the SU(n) groups (and of their algebras)\hfil\break 5. The tensor method for unitary groups, and\hb the…
This paper gives an introduction to the homotopy theory of quasi-categories. Weak equivalences between quasi-categories are characterized as maps which induce equivalences on a naturally defined system of groupoids. These groupoids…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…