Representation Theory and Higher Algebraic K-Theory

Aderemi Kuku

September 27, 2006 by Chapman and Hall/CRC
Reference - 442 Pages
ISBN 9781584886037 - CAT# C603X
Series: Chapman & Hall/CRC Pure and Applied Mathematics

was $140.00

USD$112.00

SAVE ~$28.00

Add to Wish List
FREE Standard Shipping!

Features

  • Presents higher algebraic K-theory of orders and group rings for the first time in book form
  • Explores connections between CG and higher algebraic K-theory of C for suitable categories, such as exact, symmetric monoidal, and Waldhausen
  • Collects methods that have been known to work for computations of higher K-theory of noncommutative rings, such as orders and group rings
  • Describes all higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations for finite, profinite, and compact Lie group actions
  • Obtains results on higher K-theory of orders ?, and hence group rings, for all n = 0
  • Uses computations of higher K-theory of orders that automatically yield results on higher K-theory of RG(G finite) to produce results on higher K-theory of some infinite groups
  • Provides appendices with many known computations and open problems in classical and higher algebraic K-theory of orders, group rings, and related structures
  • Summary

    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.

    Instructors

    We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.

    Request an
    e-inspection copy

    Share this Title