Related papers: On the equations defining affine algebraic groups

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…

We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…

We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed the number of generators.

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.

We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive supergroups.

In Part 1 of this study we showed, for a wide range of geometries, that the relationships between their concept-sets are fully determined by those between their (affine) automorphism groups. In this (self-contained) part, we show how this…

We give several necessary and sufficient conditions for the existence of {\it the presentation by conjugation} for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence…

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.

We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

We introduce a class of objects which we call 'affine surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples, and we define concepts related to these in…

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…

We discuss various methods and their effectiveness for solving linear equations over finitely generated abelian groups. More precisely, if $\varphi\colon G\to H$ is a homomorphism of finitely generated abelian groups and $b\in H$, we…

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…

We define a certain abstract planar algebra by generators and relations, study various aspects of its structure, and then identify it with Jones' spin planar algebra.

Each irreducible representation of the affine group of a finite field has a unique maximal inductive algebra, and it is self adjoint.

In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.

We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…