{"paper":{"title":"Continuous Fields of $C^*$-Algebras Arising from Extensions of Tensor $C^*$-Categories","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ezio Vasselli","submitted_at":"2001-01-11T14:33:55Z","abstract_excerpt":"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-algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}