Overview
Offers the only self-contained treatment of Hopf algebras, and makes Hopf algebras accessible to advanced undergraduates and beginning graduate students
Underscores importance of Hopf orders with applications to algebraic number theory, Galois module theory and the theory of formal groups
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
“The goal of this book is to introduce readers to the use of Hopf algebras in algebraic number theory and Galois module theory, in particular developing the theory of Hopf orders. … The book concludes with a chapter of open problems, making this text very suitable for a beginning graduate student to work towards the research frontier in this area. … This work very nicely complements the other texts on Hopf algebras and is a welcome addition to the literature.”
—Jan E. Grabowski, Mathematical Reviews, July, 2013
"In this book, Underwood chooses to introduce Hopf algebras in a manner most natural to a reader whose knowledge of algebra does not extend much beyond a first year graduate course."
— Alan Koch, zbMath
“The last three chapters of the book in point of fact deal with particularly attractive “arithmetical” themes such as class groups of Hopf orders. Underwood ends the book with a discussion of “Open questions and research problems.” Clearly this is very sexy stuff, and Underwood’s book will make a real impact cutting across a number of putative boundaries…"
—Michael Berg, MAA Reviews
Authors and Affiliations
About the author
Robert G. Underwood is an Associate Professor of Mathematics at Auburn University. His research interests include the classification of Hopf algebra orders in group rings and the application of Hopf orders to Galois module theory. Professor Underwood earned his PhD in Mathematics in 1992 from the State University of New York at Albany, and his Masters in Math Education in 1986, also from SUNY Albany.
Bibliographic Information
Book Title: An Introduction to Hopf Algebras
Authors: Robert G. Underwood
DOI: https://doi.org/10.1007/978-0-387-72766-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-0-387-72765-3Published: 30 August 2011
Softcover ISBN: 978-1-4899-9784-5Published: 15 August 2014
eBook ISBN: 978-0-387-72766-0Published: 28 August 2011
Edition Number: 1
Number of Pages: XIV, 273
Topics: Algebra, Commutative Rings and Algebras, Group Theory and Generalizations