Equivariant K-theory and freeness of group actions on C[*]-algebras
Author(s)
Bibliographic Information
Equivariant K-theory and freeness of group actions on C[*]-algebras
（Lecture notes in mathematics, 1274）
Springer-Verlag, c1987
- : gw
- : us
Available at / 68 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||12748711041S
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:510/P5552070069435
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Note
Bibliography: p. [329]-334
Includes index
Description and Table of Contents
Description
Freeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K-theory. This fact can be regarded as a theorem on actions on a commutative C*-algebra, namely the algebra of continuous complex-valued functions on the space. The successes of "noncommutative topology" suggest that one should try to generalize this result to actions on arbitrary C*-algebras. Lacking an appropriate definition of a free action on a C*-algebra, one is led instead to the study of actions satisfying conditions on equivariant K-theory - in the cases of spaces, simply freeness. The first third of this book is a detailed exposition of equivariant K-theory and KK-theory, assuming only a general knowledge of C*-algebras and some ordinary K-theory. It continues with the author's research on K-theoretic freeness of actions. It is shown that many properties of freeness generalize, while others do not, and that certain forms of K-theoretic freeness are related to other noncommutative measures of freeness, such as the Connes spectrum. The implications of K-theoretic freeness for actions on type I and AF algebras are also examined, and in these cases K-theoretic freeness is characterized analytically.
Table of Contents
Introduction: The commutative case.- Equivariant K-theory of C*-algebras.- to equivariant KK-theory.- Basic properties of K-freeness.- Subgroups.- Tensor products.- K-freeness, saturation, and the strong connes spectrum.- Type I algebras.- AF algebras.
by "Nielsen BookData"
