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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| Hlavní autor: | |
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| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Edice: | Lecture notes in mathematics
1274 |
| Témata: | |
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Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Equivariant K-theory and freeness of group actions on C*-algebras, N. Christopher Phillips, 1987, Berlin, Springer-Verlag, 1 vol. (VIII-371 p.), Lecture notes in mathematics, 0-387-18277-2 • Equivariant K-Theory and Freeness of Group Actions on C*-Algebras, Texte imprimé, 9783662204658 |
| Shrnutí: | 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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| Popis jednotky: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783540478683 (PDF) |
| ISSN: | 1617-9692 |
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