Representation Theory and Higher Algebraic K-Theory  book cover
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Representation Theory and Higher Algebraic K-Theory





ISBN 9781584886037
Published September 27, 2006 by Chapman and Hall/CRC
442 Pages

 
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Book Description

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-Lück assembly maps.

Table of Contents

Review of Classical Algebraic K-Theory and Representation Theory. Higher Algebraic K-Theory and Integral Representations. Mackey Functors, Equivariant Higher Algebraic K-Theory, and Equivariant Homology Theories.

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Author(s)

Biography

Kuku, Aderemi