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.
Read or Download Equivariant K-Theory and Freeness of Group Actions on C*-Algebras (Lecture Notes in Mathematics) PDF
Similar Linear books
This e-book is a compilation of a number of works from well-recognized figures within the box of illustration idea. The presentation of the subject is exclusive in supplying numerous varied issues of view, which may still makethe publication very important to scholars and specialists alike.
This is often an abridged version of the author's prior two-volume paintings, Ring thought, which concentrates on crucial fabric for a normal ring thought path whereas ommitting a lot of the cloth meant for ring concept experts. it's been praised by way of reviewers:**"As a textbook for graduate scholars, Ring concept joins the easiest.
Extra resources for Equivariant K-Theory and Freeness of Group Actions on C*-Algebras (Lecture Notes in Mathematics)