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Representation Theory and Higher Algebraic K-Theory : Chapman & Hall/CRC Pure and Applied Mathematics - Aderemi Kuku

Representation Theory and Higher Algebraic K-Theory

Chapman & Hall/CRC Pure and Applied Mathematics

Hardcover Published: 27th September 2006
ISBN: 9781584886037
Number Of Pages: 442

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Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of group rings more accessible and provides novel techniques for the computations of higher K-theory of finite and some infinite groups.

Authored by a premier authority in the field, the book begins with a careful review of classical K-theory, including clear definitions, examples, and important classical results. Emphasizing the practical value of the usually abstract topological constructions, the author systematically discusses higher algebraic K-theory of exact, symmetric monoidal, and Waldhausen categories with applications to orders and group rings and proves numerous results. He also defines profinite higher K- and G-theory of exact categories, orders, and group rings. Providing new insights into classical results and opening avenues for further applications, the book then uses representation-theoretic techniques-especially induction theory-to examine equivariant higher algebraic K-theory, their relative generalizations, and equivariant homology theories for discrete group actions. The final chapter unifies Farrell and Baum-Connes isomorphism conjectures through Davis-Luck assembly maps.

Review of classical algebraic K-theory and representation theoryp. 1
Category of representations and constructions of Grothendieck groups and ringsp. 3
Some fundamental results on K[subscript 0] of exact and Abelian categories - with applications to orders and groupringsp. 23
K[subscript 1], K[subscript 2] of orders and groupringsp. 43
Some exact sequences; negative K-theoryp. 61
Higher algebraic K-theory and integral representationsp. 85
Higher algebraic K-theory - definitions, constructions, and relevant examplesp. 87
Some fundamental results and exact sequences in higher K-theoryp. 107
Some results on higher K-theory of orders, grouprings, and modules over 'EI' categoriesp. 121
Mod-m and profinite higher K-theory of exact categories, orders, and groupingp. 225
Mackey functors, equivariant higher algebraic K-theory, and equivariant homology theoriesp. 251
Mackey, Green, and Burnside functorsp. 253
Equivariant higher algebraic K-theory together with relative generalizations - for finite group actionsp. 325
Equivariant higher K-theory for profinite group actionsp. 337
Equivariant higher K-theory for compact Lie group actionsp. 347
Equivariant higher K-theory for Waldhausen categoriesp. 359
Equivariant homology theories and higher K-theory of groupringsp. 373
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781584886037
ISBN-10: 158488603X
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 442
Published: 27th September 2006
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.5 x 15.6  x 3.0
Weight (kg): 0.79
Edition Number: 1

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