| Equivariant K-Theory and Freeness of Group Actions on C*-Algebras 1987 Edition Contributor(s): Phillips, N. Christopher (Author) |
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ISBN: 3540182772 ISBN-13: 9783540182771 Publisher: Springer OUR PRICE: $56.95 Product Type: Paperback - Other Formats Published: September 1987 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Mathematics | Topology - General - Mathematics | Geometry - General |
| Dewey: 512.55 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.78" H x 6.14" W x 9.21" (1.17 lbs) 374 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |