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.|Representation Theory and Higher Algebraic K-Theory | Mathematics
