Michel Broué: On Characters of Finite Groups

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Cover: 9789811068775 | On Characters of Finite Groups | Michel Broué | Buch | Englisch | 2018

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Sprache: Englisch

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Beschreibung

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).

Über den Autor

Michel Broué is Emeritus Exceptional Professor of Mathematics at the University Paris-Diderot Paris 7. He has been the Director of the Institut Henri-Poincaré in Paris (1999-2009), and the Director of the Department of Mathematics and Computer Science (DMI) at the École normale supérieure (1986-1993)

He is a Foreign Honorary Member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, a Senior Member of the Institut Universitaire de France, and a frequent visitor to many institutions in the world.

He is the Editor-in-chief of the Journal of Algebra, and a member of several editorial boards. His main research area is Algebra and Representation Theory, in particular of finite and algebraic groups.

Zusammenfassung

Reveals the beauty of character theory of finite groups

Familiarizes readers with the language of categories

Offers readers broader coverage than books that focus almost exclusively on groups

Inhaltsverzeichnis

Tensor Product.-On Representation.-Characteristic 0 representations.-Playing with the base field.- Induction, restriction.- Brauer's theorem and some applications.- Graded representations and characters.- Drinfeld Double.- Appendix A. Basics on Finite Groups.- Appendix B. Assumed results on Galois theory.- Appendix C. Integral elements.- Appendix D. Noetherian rings and modules.- Appendix E. The language of categories and functors.- Bibliography 211.-Index

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	264
Reihe:	Mathematical Lectures from Peking University
Inhalt:	xvi 246 S. 4 s/w Illustr. 5 farbige Illustr. 246 p. 9 illus. 5 illus. in color.
ISBN-13:	9789811068775
ISBN-10:	9811068771
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Broué, Michel
Auflage:	1st ed. 2017
Hersteller:	Springer Singapore Springer Nature Singapore Mathematical Lectures from Peking University
Maße:	241 x 160 x 20 mm
Von/Mit:	Michel Broué
Erscheinungsdatum:	29.01.2018
Gewicht:	0,565 kg

preigu-id: 111058995