Continuous fields of C*-algebras arising from extensions of tensor C*-categories

摘要

The notion of extension of a given C*-category C by a C*-algebra A is introduced. In the commutative case A = C(Omega), the objects of the extension category are interpreted as fiber bundles over Omega of objects belonging to the initial category. It is shown that the Doplicher-Roberts algebra (DR-algebra in the following) associated to an object in the extension of a strict tensor C*-category is a continuous field of DR-algebras coming from the initial one. In the case of the category of the hermitian vector bundles over Omega the general result implies that the DR-algebra of a vector bundle is a continuous field of Cuntz algebras. Some applications to Pimsner C*-algebras are given. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 36]