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Equivariant K-theory and freeness of group actions on C*-algebras

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 spa...

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Autor principal: Phillips, N Christopher
Lenguaje:eng
Publicado: Springer 1987
Materias:
Acceso en línea:https://dx.doi.org/10.1007/BFb0078657
http://cds.cern.ch/record/1691550
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author Phillips, N Christopher
author_facet Phillips, N Christopher
author_sort Phillips, N Christopher
collection CERN
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.
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spelling cern-16915502021-04-21T21:09:00Zdoi:10.1007/BFb0078657http://cds.cern.ch/record/1691550engPhillips, N ChristopherEquivariant K-theory and freeness of group actions on C*-algebrasMathematical Physics and MathematicsFreeness 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.Springeroai:cds.cern.ch:16915501987
spellingShingle Mathematical Physics and Mathematics
Phillips, N Christopher
Equivariant K-theory and freeness of group actions on C*-algebras
title Equivariant K-theory and freeness of group actions on C*-algebras
title_full Equivariant K-theory and freeness of group actions on C*-algebras
title_fullStr Equivariant K-theory and freeness of group actions on C*-algebras
title_full_unstemmed Equivariant K-theory and freeness of group actions on C*-algebras
title_short Equivariant K-theory and freeness of group actions on C*-algebras
title_sort equivariant k-theory and freeness of group actions on c*-algebras
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BFb0078657
http://cds.cern.ch/record/1691550
work_keys_str_mv AT phillipsnchristopher equivariantktheoryandfreenessofgroupactionsoncalgebras