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Representation Theory and Higher Algebraic K-Theory 27.0%OFF

Representation Theory and Higher Algebraic K-Theory

by Aderemi Kuku

  • ISBN

    :  

    9781584886037

  • Publisher

    :  

    Chapman & Hall/crc

  • Subject

    :  

    Mathematics

  • Binding

    :  

    Hardcover

  • Pages

    :  

    442

  • Year

    :  

    927

5329.0

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  • 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-Luck assembly maps.

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