An Introduction to Hopf Algebras
(Sprache: Englisch)
This book offers a unique self-contained introduction to group and ring theory, and thoroughly treats the concept of the spectrum of a ring and the Zariski topology, helping the reader transition smoothly from basic abstract algebra to Hopf algebras.
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Produktinformationen zu „An Introduction to Hopf Algebras “
This book offers a unique self-contained introduction to group and ring theory, and thoroughly treats the concept of the spectrum of a ring and the Zariski topology, helping the reader transition smoothly from basic abstract algebra to Hopf algebras.
Klappentext zu „An Introduction to Hopf Algebras “
Only book on Hopf algebras aimed at advanced undergraduates
Inhaltsverzeichnis zu „An Introduction to Hopf Algebras “
Preface.- Some Notation.- 1. The Spectrum of a Ring.-2. The Zariski Topology on the Spectrum.-3. Representable Group Functors.-4. Hopf Algebras. -5. Larson Orders.-6. Formal Group Hopf Orders.-7. Hopf Orders in KC_p.-8. Hopf Orders in KC_{p^2}.-9. Hopf Orders in KC_{p^3}.-10. Hopf Orders and Galois Module Theory.-11. The Class Group of a Hopf Order.-12. Open Questions and Research Problems.-Bibliography.-Index.Autoren-Porträt von Robert G. Underwood
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.
Bibliographische Angaben
- Autor: Robert G. Underwood
- 2014, 2011, XIV, 273 Seiten, Maße: 15,7 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1489997849
- ISBN-13: 9781489997845
Sprache:
Englisch
Rezension zu „An Introduction to Hopf Algebras “
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
Pressezitat
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
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