---

＜E-Book＞
Equivariant K-Theory and Freeness of Group Actions on C*-Algebras / by N. Christopher Phillips
(Lecture Notes in Mathematics. ISSN:16179692 ; 1274)

Edition	1st ed. 1987.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1987
Size	X, 374 p : online resource
Authors	*Phillips, N. Christopher author SpringerLink (Online service)
Subjects	LCSH:Algebraic topology FREE:Algebraic Topology
Notes	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 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 HTTP:URL=https://doi.org/10.1007/BFb0078657

 Similar Items