From Rings and Modules to Hopf Algebras : One Flew Over the Algebraist's Nest

Michel Broué

ISBN 10: 303150061X / ISBN 13: 9783031500619

Edité par Springer, Springer, 2024

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups.Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory - whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld-Lusztig double of a group algebra, appearing for the first time in a textbook at this level.Based on over twenty years of teaching various aspects of algebra, mainly at the École Normale Supérieure (Paris) and at Peking University, the book reflects the audiences of the author's courses. In particular, foundations of abstract algebra, like linear algebra and elementary group theory, are assumed of the reader. Each of the of four parts can be used for a course - with a little ad hoc complement on the language of categories. Thanks to its rich choice of topics, the book can also serve students as a reference throughout their studies, from undergraduate to advanced graduate level.

N° de réf. du vendeur 9783031500619

Détails bibliographiques

• Titre: From Rings and Modules to Hopf Algebras : One Flew Over the Algebraist's Nest
• Éditeur: Springer, Springer
• Date de parution: 2024
• Langue: anglais
• ISBN à 10 chiffres: 303150061X
• ISBN à 13 chiffres: 9783031500619
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 33 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 33 millimètres de profondeur
• Poids: 1073 grammes

A propos de ce titre

Synopsis

This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups.
Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory ― whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld–Lusztig double of a group algebra, appearing for the first time in a textbook at this level.
Based on over twenty years of teaching various aspects of algebra, mainly at the École Normale Supérieure (Paris) and at Peking University, the book reflects the audiences of the author's courses. In particular, foundations of abstract algebra, like linear algebra and elementary group theory, are assumed of the reader. Each of the of four parts can be used for a course ― with a little ad hoc complement on the language of categories. Thanks to its rich choice of topics, the book can also serve students as a reference throughout their studies, from undergraduate to advanced graduate level.

À propos de l'auteur

Michel Broué is a distinguished French mathematician specialising in algebra. He is known for his work on modular representations of finite groups (where a famous conjecture bears his name), on the "generic approach" to representations of finite reductive groups, as well as for work on related areas like cyclotomic Hecke algebras. During a career spanning half a century, he has been the editor-in-chief of the Journal of Algebra (2001-2017), the director of the Department of Mathematics and Computer Science of the École Normale Supérieure and the director of the Institut Henri Poincaré (1999-2009).