Extensions of C∗-algebras and translation invariant asymptotic homomorphisms
DOI:
https://doi.org/10.7146/math.scand.a-15018Abstract
Let A, B be C∗-algebras; A separable, B σ-unital and stable. We introduce a notion of translation invariance for asymptotic homomorphisms from SA=C0(R)⊗A to B and show that the Connes-Higson construction applied to any extension of A by B is homotopic to a translation invariant asymptotic homomorphism. In the other direction we give a construction which produces extensions of A by B out of such a translation invariant asymptotic homomorphism. This leads to our main result; that the homotopy classes of extensions coincide with the homotopy classes of translation invariant asymptotic homomorphisms.Downloads
Published
2007-03-01
How to Cite
Manuilov, V., & Thomsen, K. (2007). Extensions of C∗-algebras and translation invariant asymptotic homomorphisms. MATHEMATICA SCANDINAVICA, 100(1), 131–160. https://doi.org/10.7146/math.scand.a-15018
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