Fundamentals of Hopf Algebras

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book Fundamentals of Hopf Algebras by Robert G. Underwood, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Robert G. Underwood ISBN: 9783319189918
Publisher: Springer International Publishing Publication: June 10, 2015
Imprint: Springer Language: English
Author: Robert G. Underwood
ISBN: 9783319189918
Publisher: Springer International Publishing
Publication: June 10, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Principles of Osteoimmunology by Robert G. Underwood
Cover of the book The Statistical Stability Phenomenon by Robert G. Underwood
Cover of the book Polyoxometalate-Based Assemblies and Functional Materials by Robert G. Underwood
Cover of the book Recent Advances in Information Systems and Technologies by Robert G. Underwood
Cover of the book Cellular Automata and Discrete Complex Systems by Robert G. Underwood
Cover of the book Digital Transformation in Financial Services by Robert G. Underwood
Cover of the book Introduction to Statistical Methods in Pathology by Robert G. Underwood
Cover of the book Peyronie’s Disease by Robert G. Underwood
Cover of the book Combined Cycle Driven Efficiency for Next Generation Nuclear Power Plants by Robert G. Underwood
Cover of the book Gamification in Learning and Education by Robert G. Underwood
Cover of the book Innovations in Culture and Development by Robert G. Underwood
Cover of the book High Performance Computing by Robert G. Underwood
Cover of the book Computational Science – ICCS 2018 by Robert G. Underwood
Cover of the book Advances in Intelligent Informatics, Smart Technology and Natural Language Processing by Robert G. Underwood
Cover of the book Antibacterials by Robert G. Underwood
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy