On Characters of Finite Groups (Mathematical Lectures from Peking University) - Hardcover

Broué, Michel

Hardcover

ISBN 10: 9811068771 ISBN 13: 9789811068775

Verlag: Springer, 2018

Inhaltsangabe

<P>THIS BOOK EXPLORES THE CLASSICAL AND BEAUTIFUL CHARACTER THEORY OF FINITE GROUPS. IT DOES IT BY USING SOME RUDIMENTS OF THE LANGUAGE OF CATEGORIES. ORIGINALLY EMERGING FROM TWO COURSES OFFERED AT PEKING UNIVERSITY (PKU), PRIMARILY FOR THIRD-YEAR STUDENTS, IT IS NOW BETTER SUITED FOR GRADUATE COURSES, AND PROVIDES BROADER COVERAGE THAN BOOKS THAT FOCUS ALMOST EXCLUSIVELY ON GROUPS.</P><P>THE BOOK PRESENTS THE BASIC TOOLS, NOTIONS AND THEOREMS OF CHARACTER THEORY (INCLUDING A NEW TREATMENT OF THE CONTROL OF FUSION AND ISOMETRIES), AND INTRODUCES READERS TO THE CATEGORICAL LANGUAGE AT SEVERAL LEVELS. IT INCLUDES AND PROVES THE MAJOR RESULTS ON CHARACTERISTIC ZERO REPRESENTATIONS WITHOUT ANY ASSUMPTIONS ABOUT THE BASE FIELD. THE BOOK INCLUDES A DEDICATED CHAPTER ON GRADED REPRESENTATIONS AND APPLICATIONS OF POLYNOMIAL INVARIANTS OF FINITE GROUPS, AND ITS CLOSING CHAPTER ADDRESSES THE MORE RECENT NOTION OF THE DRINFELD DOUBLE OF A FINITE GROUP AND THE CORRESPONDING REPRESENTATION OF GL_2(Z).<BR></P>

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Críticas

“The book is written by one of the best character theorists, and he has done a great job. I am sure, teachers and students interested in character theory both enjoy reading this book.” (Mohammad-Reza Darafsheh, zbMATH 1391.20001, 2018)

Reseña del editor

This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups.

The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2018
• ISBN 10: 9811068771
• ISBN 13: 9789811068775
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 264