𝐶*-algebras generalizing both relative Cuntz-Pimsner and Doplicher-Roberts algebras

Kwaśniewski, B.

doi:10.1090/S0002-9947-2012-05748-5

$C^*$-algebras generalizing both relative Cuntz-Pimsner and Doplicher-Roberts algebras
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Abstract:

We introduce and analyse the structure of $C^*$-algebras arising from ideals in right tensor $C^*$-precategories, which naturally unify the approaches based on Hilbert $C^*$-modules and $C^*$-categories with tensor structure. We establish an explicit intrinsic construction of the algebras considered, prove a number of key results such as a structure theorem and a gauge-invariant uniqueness theorem, and describe the gauge-invariant ideal structure. These results give a new insight into the corresponding statements for relative Cuntz-Pimsner algebras and are applied to Doplicher-Roberts algebras associated with $C^*$-correspondences.

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