The concern of this paper is to investigate the structure of skew polynomial rings (Ore
extensions) of the form T= R [θ; σ, δ] where σ and δ are both nontrivial, and in particular to …

1.1. Let C be a symmetrizable Cartan matrix. One may associate [3, 4] to C a Hopf algebra
U&g,) which is a quantized version of the enveloping algebra U (g,) of the Kac-Moody Lie …

There has been continued interest in skew polynomial rings and related constructions since
Ore's initial studies in the 1930s. New examples not covered by previous analyses have …

Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix.
This chapter should be used as reference material and should be consulted as needed. A …

This article describes recent work on new classes of non-commutative algebras which have
been dubbed quantum algebras, quantum groups, and quantized enveloping algebras. The …

We prove that every coalgebra C is a direct sum of coalgebras in such a way that the
summands correspond to the connected components of the Ext quiver of the simple …

In this paper we examine a variety of algebraic contexts in which the quantum Yang–Baxter
equation arises, and describe methods for generating new solutions from given ones. The …

Ce travail est consacré aux groupes d'automorphismes de certaines algebres quantiques de
dimension 2 ou 3. Dans la théorie classique des algebres enveloppantes, si désigne …

In this paper we lay the foundation for studying quantum groups as part of algebraic
deformation theory by introducing the quantum symmetric group and the concept of quantum …

Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic
zero on commutative domains were classified recently by the authors in 18. The answer …