Continuous Fields of $C^*$-Algebras Arising from Extensions of Tensor $C^*$-Categories

Ezio Vasselli

Continuous Fields of $C^$-Algebras Arising from Extensions of Tensor $C^$-Categories

Operator Algebras 2011-11-18 v1

Authors: Ezio Vasselli

Abstract

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.

Keywords

c*-categories extensions continuous fields doplicher-roberts algebra tensor c*-categories cuntz algebras pimsner c*-algebras

Cite

@article{arxiv.math/0101099,
  title  = {Continuous Fields of $C^*$-Algebras Arising from Extensions of Tensor $C^*$-Categories},
  author = {Ezio Vasselli},
  journal= {arXiv preprint arXiv:math/0101099},
  year   = {2011}
}

Comments

28 pages, uses xy.sty, submitted to Journal of Functional Analysis