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- catalog abstract "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.".
- catalog contributor b1857867.
- catalog created "c1987.".
- catalog date "1987".
- catalog date "c1987.".
- catalog dateCopyrighted "c1987.".
- catalog description "Bibliography: p. [329]-334.".
- catalog description "Contents: Introduction: The Commutative Case -- Equivariant K-Theory of C*-Algebras -- Introduction 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 -- References -- Author Reference Index -- Index of Notation -- Subject Index.".
- catalog 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.".
- catalog extent "viii, 371 p. ;".
- catalog hasFormat "Equivariant K-theory and freeness of group actions on C*-algebras.".
- catalog identifier "0387182772 (U.S.) :".
- catalog identifier "3540182772".
- catalog isFormatOf "Equivariant K-theory and freeness of group actions on C*-algebras.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1274.".
- catalog isPartOf "Lecture notes in mathematics ; 1274".
- catalog issued "1987".
- catalog issued "c1987.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Equivariant K-theory and freeness of group actions on C*-algebras.".
- catalog subject "510 s 512/.55 19".
- catalog subject "Algebraic topology.".
- catalog subject "C*-algebras.".
- catalog subject "K-theory.".
- catalog subject "Lie groups.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1274 QA612.33".
- catalog tableOfContents "Contents: Introduction: The Commutative Case -- Equivariant K-Theory of C*-Algebras -- Introduction 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 -- References -- Author Reference Index -- Index of Notation -- Subject Index.".
- catalog title "Equivariant K-theory and freeness of group actions on C*-algebras / N. Christopher Phillips.".
- catalog type "text".