Extensions of C* - algebras and translation invariant asymptotic homomorphisms
- Autores: Vladimir Manuilov, Klaus Thomsen
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 100, Nº 1, 2007, págs. 131-160
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15018
- Enlaces
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Resumen
Let A, B be C* algebras; A separable, B [O]-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 directionwe 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.
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