Fundamentals of Hopf Algebras (Universitext) 2015th Edition by Robert G. Underwood (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “The goal of the book under review is to introduce graduate students to some basic results on coalgebras, bialgebras, Hopf algebras, and their applications. The book may be used as the main text or as a supplementary text for a graduate course. … This book should be very useful as a first introduction for someone who wants to learn about Hopf algebras and their applications.” (Jörg Feldvoss, zbMATH 1341.16034, 2016) From the Back Cover 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. About the Author Robert G. Underwood, MS, PhD, is a professor of Mathematics at Auburn University at Montgomery and author of Introduction to Hopf Algebras © Springer 2011. The author’s course notes which contribute strongly to this present book have been used in his modern algebra class since 2008. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book addresses the needs of those who want a gentle introduction to Hopf Algebras. It was ideal for me since my math education is 4 decades old and my background in algebra is weak. A Hopf algebra is an algebra that is also a coalgebra and has some extra structure. So it makes sense to present the definition in 3 chapters as professor Underwood does. The first chapter defines algebras and coalgebras. The format is the standard pattern: definition, followed by examples, followed by theorems. There is plenty of hand-holding in the proofs. The second chapter is on bialgebras, that is, algebras that are also coalgebras. The third chapter is on Hopf algebras, that is bialgebras with that extra structure I mentioned. The fourth chapter is on some applications of Hopf algebras. There are plenty of exercises. Since this was my first reading of the book, I only reached for the low-hanging fruit. These seemed to me to induce tedium rather than understanding. However, the problems I didn’t attack may be the better ones.

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Free Download Fundamentals of Hopf Algebras (Universitext) 2015th Edition in PDF format
Fundamentals of Hopf Algebras (Universitext) 2015th Edition PDF Free Download
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Fundamentals of Hopf Algebras (Universitext) 2015th Edition 2015 PDF Free Download
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