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Noetherian Semigroup Algebras

  • Eric Jespers
  • Jan Okniński

Part of the Algebra and Applications book series (AA, volume 7)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Eric Jespers, Jan Okniński
    Pages 1-5
  3. Eric Jespers, Jan Okniński
    Pages 7-35
  4. Eric Jespers, Jan Okniński
    Pages 37-61
  5. Eric Jespers, Jan Okniński
    Pages 63-115
  6. Eric Jespers, Jan Okniński
    Pages 117-147
  7. Eric Jespers, Jan Okniński
    Pages 149-175
  8. Eric Jespers, Jan Okniński
    Pages 177-195
  9. Eric Jespers, Jan Okniński
    Pages 197-255
  10. Eric Jespers, Jan Okniński
    Pages 257-289
  11. Eric Jespers, Jan Okniński
    Pages 291-341
  12. Back Matter
    Pages 343-362

About this book

Introduction

Within the last decade, semigroup theoretical methods have occurred naturally in many aspects of ring theory, algebraic combinatorics, representation theory and their applications. In particular, motivated by noncommutative geometry and the theory of quantum groups, there is a growing interest in the class of semigroup algebras and their deformations.

This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes of quadratic algebras and algebras related to group rings of polycyclic-by-finite groups. These give new classes of Noetherian algebras of small Gelfand-Kirillov dimension. The focus is on the interplay between their combinatorics and the algebraic structure. This yields a rich resource of examples that are of interest not only for the noncommutative ring theorists, but also for researchers in semigroup theory and certain aspects of group and group ring theory. Mathematical physicists will find this work of interest owing to the attention given to applications to the Yang-Baxter equation.

Keywords

Algebraic structure Gelfand-Kirillov dimension Group theory Noetherian and PI algebra Representation theory maximal order ring theory semigroup algebra semigroup, group

Authors and affiliations

  • Eric Jespers
    • 1
  • Jan Okniński
    • 2
  1. 1.Vrije Universiteit BrusselBrusselsBelgium
  2. 2.Warsaw UniversityWarsawPoland

Bibliographic information