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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Topology

• Full title: Equivariant K-Theory and Freeness of Group Actions on C*-Algebras
• Author: N. Christopher Phillips
• Language: English
• Binding: Paperback
• Number of pages: 374
• EAN: 9783540182771
• ISBN: 3540182772
• ID: 05273629
• Publisher: Springer, Berlin
• Weight: 573 g
• Dimensions: 234 × 156 × 19 mm

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