On the KK-theory of strongly self-absorbing C-algebras

Authors

  • Marius Dadarlat
  • Wilhelm Winter

DOI:

https://doi.org/10.7146/math.scand.a-15086

Abstract

Let D and A be unital and separable C-algebras; let D be strongly self-absorbing. It is known that any two unital -homomorphisms from D to AD are approximately unitarily equivalent. We show that, if D is also K1-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of D is asymptotically inner. Moreover, the space of automorphisms of D is compactly-contractible (in the point-norm topology) in the sense that for any compact Hausdorff space X, the set of homotopy classes [X,(Aut(D)] reduces to a point. The respective statement holds for the space of unital endomorphisms of D. As an application, we give a description of the Kasparov group KK(D,AD) in terms of -homomorphisms and asymptotic unitary equivalence. Along the way, we show that the Kasparov group KK(D,AD) is isomorphic to K0(AD).

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Published

2009-03-01

How to Cite

Dadarlat, M., & Winter, W. (2009). On the KK-theory of strongly self-absorbing C-algebras. MATHEMATICA SCANDINAVICA, 104(1), 95–107. https://doi.org/10.7146/math.scand.a-15086

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Articles