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Phillips

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

Medium: Buch
ISBN: 978-3-540-18277-1
Verlag: Springer Berlin Heidelberg
Erscheinungstermin: 23.09.1987
Lieferfrist: bis zu 10 Tage

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.


Produkteigenschaften


  • Artikelnummer: 9783540182771
  • Medium: Buch
  • ISBN: 978-3-540-18277-1
  • Verlag: Springer Berlin Heidelberg
  • Erscheinungstermin: 23.09.1987
  • Sprache(n): Englisch
  • Auflage: 1987
  • Serie: Lecture Notes in Mathematics
  • Produktform: Kartoniert
  • Gewicht: 575 g
  • Seiten: 374
  • Format (B x H x T): 155 x 235 x 21 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

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.