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Trivialization of 𝒞 ( X ) -algebras with strongly self-absorbing fibres

Marius DadarlatWilhelm Winter — 2008

Bulletin de la Société Mathématique de France

Suppose A is a separable unital 𝒞 ( X ) -algebra each fibre of which is isomorphic to the same strongly self-absorbing and K 1 -injective C * -algebra 𝒟 . We show that A and 𝒞 ( X ) 𝒟 are isomorphic as 𝒞 ( X ) -algebras provided the compact Hausdorff space X is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

Extensions of certain real rank zero C * -algebras

Marius DadarlatTerry A. Loring — 1994

Annales de l'institut Fourier

G. Elliott extended the classification theory of A F -algebras to certain real rank zero inductive limits of subhomogeneous C * -algebras with one dimensional spectrum. We show that this class of C * -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the K 1 -group. Perturbation and lifting results are provided for certain subhomogeneous C * -algebras.

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