Equivariant K-Theory and Freeness of Group Actions on C*-Algebras

  • Authors
  • N.¬†Christopher¬†Phillips

Part of the Lecture Notes in Mathematics book series (LNM, volume 1274)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. N. Christopher Phillips
    Pages 1-11
  3. N. Christopher Phillips
    Pages 12-67
  4. N. Christopher Phillips
    Pages 68-130
  5. N. Christopher Phillips
    Pages 131-166
  6. N. Christopher Phillips
    Pages 167-188
  7. N. Christopher Phillips
    Pages 189-235
  8. N. Christopher Phillips
    Pages 236-274
  9. N. Christopher Phillips
    Pages 275-285
  10. N. Christopher Phillips
    Pages 286-328
  11. Back Matter
    Pages 329-371

About this book

Introduction

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.

Keywords

K-theory algebra group action lie group

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078657
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18277-1
  • Online ISBN 978-3-540-47868-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book