Title: Equivariant K-theory and freeness of group actions on C*-algebras
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.
Subjects: C*-algebras, K-theory, Lie groups, Funkcionálanalízis, K-theorie, C*-algebra's, C*-algèbres, Groupes de Lie, Nemkommutativ dinamikus rendszerek, K-Algebra, C-Stern-Algebra, K-théorie, Matematika, Äquivariante K-Theorie, Lie-Gruppe, K-elmélet, C*-algebra, Operátoralgebra, C algebras, Mathematics, Algebraic topology