Overview
- The simple tools described provide a new way of looking at group representation theory and its applications
- Offers an insight into the mind of one of the great mathematicians
- Much of the work described has not previously appeared in book form
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2233)
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Table of contents (10 chapters)
Keywords
About this book
This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science.
The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.Reviews
“The book is clearly written and presents many little known facts about group matrices. No other book deals so thoroughly with this topic.” (John D. Dixon, zbMATH 1458.20001, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Group Matrices, Group Determinants and Representation Theory
Book Subtitle: The Mathematical Legacy of Frobenius
Authors: Kenneth W. Johnson
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-28300-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-28299-8Published: 09 November 2019
eBook ISBN: 978-3-030-28300-1Published: 08 November 2019
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XXV, 384
Number of Illustrations: 5 b/w illustrations
Topics: Group Theory and Generalizations, Associative Rings and Algebras, Combinatorics, Probability Theory and Stochastic Processes