Equivariant K-Theory and Freeness of Group Actions on C*-Algebras (Paperback, 1987 ed.)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 1274
Release date:	September 1987
First published:	1987
Authors:	N.Christopher Phillips
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Paperback
Pages:	374
Edition:	1987 ed.
ISBN-13:	978-3-540-18277-1
Categories:	Books > Science & Mathematics > Mathematics > Topology > Algebraic topology Promotions
LSN:	3-540-18277-2
Barcode:	9783540182771

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