Fundamentals of Hopf Algebras

  • Robert G. Underwood

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Robert G. Underwood
    Pages 1-34
  3. Robert G. Underwood
    Pages 35-66
  4. Robert G. Underwood
    Pages 67-106
  5. Robert G. Underwood
    Pages 107-144
  6. Back Matter
    Pages 145-150

About this book

Introduction

This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras.  The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras.  The book may be used as the main text or as a supplementary text for a graduate algebra course.  Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields, and linearly recursive sequences.

The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises.  Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.

Keywords

Galois module theory Hopf algebras bialgebras coalgebras finite fields knot theory

Authors and affiliations

  • Robert G. Underwood
    • 1
  1. 1.Department of Mathematics and Computer ScienceAuburn University at MontgomeryMontgomeryUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-18991-8
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-18990-1
  • Online ISBN 978-3-319-18991-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book