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 Radio Frequency Multiple Access Techniques Made Easy by Robert G. Underwood
Cover of the book Progress in Partial Differential Equations by Robert G. Underwood
Cover of the book Fractal Apertures in Waveguides, Conducting Screens and Cavities by Robert G. Underwood
Cover of the book Discovery Science by Robert G. Underwood
Cover of the book Current Trends in Preparatory Proceedings by Robert G. Underwood
Cover of the book Sociopolitical Dimensions of Mathematics Education by Robert G. Underwood
Cover of the book Evolving Narratives of Hazard and Risk by Robert G. Underwood
Cover of the book Mapping Asia: Cartographic Encounters Between East and West by Robert G. Underwood
Cover of the book Towards the Humanisation of Birth by Robert G. Underwood
Cover of the book Information Technology in Biomedicine by Robert G. Underwood
Cover of the book Relativity and Gravitation by Robert G. Underwood
Cover of the book Algebraic Combinatorics by Robert G. Underwood
Cover of the book Etiology of Acute Leukemias in Children by Robert G. Underwood
Cover of the book Machine Learning and Knowledge Discovery in Databases by Robert G. Underwood
Cover of the book Water Scarcity and Ways to Reduce the Impact 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