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Download E-books Equivariant K-Theory and Freeness of Group Actions on C*-Algebras (Lecture Notes in Mathematics) PDF

By N. Christopher Phillips

Freeness of an motion of a compact Lie team on a compact Hausdorff house is akin to an easy at the corresponding equivariant K-theory. This truth may be considered as a theorem on activities on a commutative C*-algebra, specifically the algebra of continuing complex-valued capabilities at the area. The successes of "noncommutative topology" recommend that one should still attempt to generalize this end result to activities on arbitrary C*-algebras. missing a suitable definition of a unfastened motion on a C*-algebra, one is led as an alternative to the examine of activities gratifying stipulations on equivariant K-theory - within the circumstances of areas, easily freeness. the 1st 3rd of this publication is a close exposition of equivariant K-theory and KK-theory, assuming just a basic wisdom of C*-algebras and a few traditional K-theory. It keeps with the author's examine on K-theoretic freeness of activities. it truly is proven that many houses of freeness generalize, whereas others don't, and that definite types of K-theoretic freeness are regarding different noncommutative measures of freeness, equivalent to the Connes spectrum. the results of K-theoretic freeness for activities on variety I and AF algebras also are tested, and in those instances K-theoretic freeness is characterised analytically.

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