Locally AH-Algebras

ISBN-13: 9781470414665 / Angielski

Huaxin Lin

Opis

A unital separable $C^ast$-algebra, $A$ is said to be locally AH with no dimension growth if there is an integer $d>0$ satisfying the following: for any $epsilon >0$ and any compact subset ${mathcal F}subset A,$ there is a unital $C^ast$-subalgebra, $B$ of $A$ with the form $PC(X, M_n)P$, where $X$ is a compact metric space with covering dimension no more than $d$ and $Pin C(X, M_n)$ is a projection, such that $mathrm(a, B)

Spis treści

• Introduction
• Preliminaries
• Definition of ${\mathcal C}_g$ $C^\ast$-algebras in ${\mathcal C}_g$
• Regularity of $C^\ast$-algebras in ${\mathcal C}_1$
• Traces
• The unitary group ${\mathcal Z}$-stability
• General existence theorems
• The uniqueness statement and the existence theorem for Bott map
• The basic homotopy lemma
• The proof of the uniqueness theorem 10.4
• The reduction
• Appendix
• Bibliography