Related papers: Equational quasigroup definitions
The quasiparticle wavefunction of a many-electron system is traditionally defined as the eigenfunction of the quasiparticle eigenvalue equation involving the self-energy. In this article a new concept of a quasiparticle wavefunction is…
A finite quantum hypergroup is a finite-dimensional unital algebra $A$ over the field of complex numbers. There is a coproduct on $A$, a coassociative map from $A$ to $A\otimes A$ assumed to be unital, but it is not required to be an…
We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup.
We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups.
We are interested in formulas for the number of elements in certain classes of numerical semigroups
A semigroup $S$ is an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove that every nontrivial semigroup in the standard language $\{\cdot\}$ is not an equational domain.
We study different notions of quasiconvexity for a subgroup $H$ of a relatively hyperbolic group $G.$ The first result establishes equivalent conditions for $H$ to be relatively quasiconvex. As a corollary we obtain that the relative…
The definition of Suzuki groups over rings is given by means of an explicit description as a difference-algebraic group. For a (not necessarily perfect) field with more than two elements this construction produces a simple group.
Equivalencies of many basic elementary inequalities are given
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
A semigroup $S$ is an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove that if an inverse semigroup $S$ is an equational domain in the extended language $\{\cdot,{}^{-1}\}\cup\{s|s\in S\}$ then $S$ is…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
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…
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…
Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…
We concern with various aspects of equilibrium and non-equilibrium quantum field theory.
Formal languages based on the multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.