On the Homotopy Type of the Unitary Group and the Grassmann Space of Purely Infinite Simple C*-Algebras |
| |
Authors: | Shuang Zhang |
| |
Affiliation: | (1) Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, U.S.A. |
| |
Abstract: | We completely determine the homotopy groups n(.) of the unitary group and the space of projections of purely infinite simple C*-algebras in terms of K-theory. We also prove that the unitary group of a purely infinite simple C*-algebra A is a contractible topological space if and only if K0(A) = K1(A) = {0}, and again if and only if the unitary group of the associated generalized Calkin algebra L(HA) / K(HA) is contractible. The well-known Kuiper's theorem is extended to a new class of C*-algebras. |
| |
Keywords: | C*-algebras homotopy groups unitaries projections |
本文献已被 SpringerLink 等数据库收录! |
|