On the Homotopy Type of the Unitary Group and the Grassmann Space of Purely Infinite Simple C*-Algebras |
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Authors: | Shuang Zhang |
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Institution: | (1) Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, U.S.A. |
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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. |
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Keywords: | C
*-algebras homotopy groups unitaries projections |
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