ENGLISH

From Rings and Modules to Hopf Algebras

By Michel Broué

Book information

Publisher
Springer Nature Switzerland
Year
2024
ISBN
9783031500619, 9783031500626
DOI
10.1007/978-3-031-50062-6
Language
english
Format
PDF
Filesize
9 MB (9100513 bytes)
Edition
1
Pages
533\528
Topic
Mathematics Algebra
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-02-01 15:30:54
Artin's theoremBrauer's theoremDedekind ringDrinfeld-Lusztig doubleGalois TheoryGraded representationsidealsModulesMonoidal categoryNullstellensatzPolynomial ringsPrincipal ideal domainProjective representationsRepresentations of finite groups

Description

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.

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