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

TL;DR

This paper introduces a new class of C*-algebras from ideals in right tensor C*-precategories, unifying and extending the understanding of relative Cuntz-Pimsner and Doplicher-Roberts algebras through explicit constructions and key structural theorems.

Contribution

It provides a novel intrinsic construction and structural analysis of these generalized C*-algebras, offering new insights into their ideal and gauge-invariant properties.

Findings

Established a structure theorem for the new C*-algebras

Proved a gauge-invariant uniqueness theorem

Described the gauge-invariant ideal structure

Abstract

We introduce and analyse the structure of C*-algebras arising from ideals in right tensor C*-precategories, which naturally generalize both relative Cuntz-Pimsner and Doplicher-Roberts algebras. We establish an explicit intrinsic construction of the considered algebras and a number of key results such as structure theorem, gauge-invariant uniqueness theorem or description of the gauge-invariant ideal structure. In particular, these statements give a new insight into the corresponding results for relative Cuntz-Pimsner algebras and are applied to Doplicher-Roberts associated to C*-correspondences.