Representation Theory and Higher Algebraic K-Theory
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A01=Aderemi Kuku
Abelian Category
Abelian Group
advanced group ring computations
algebraic structures
assembly map conjectures
Author_Aderemi Kuku
Burnside Ring
Cartesian Square
Category=PB
Central Division Algebra
Commutative Diagram
Commutative Regular Ring
Commutative Ring
Dedekind Domain
Division Algebra
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
equivariant homology
Exact Category
Exact Functor
Exact Sequence
Free Abelian Monoid
Full Subcategory
Galois Extension
Green Functor
Homotopy Equivalence
induction theory
Mackey functors
Noetherian Ring
Open Normal Subgroups
profinite groups
Serre Subcategory
Short Exact Sequence
Snake Lemma
Split Exact Sequence
Symmetric Monoidal Category
Product details
- ISBN 9781584886037
- Weight: 793g
- Dimensions: 156 x 234mm
- Publication Date: 27 Sep 2006
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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-Lück assembly maps.
Kuku, Aderemi
