Classification of Certain C*-Algebras Generated by Two Partitions of Unity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911132214624256 |
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| author | Schäfer, Björn |
| author_facet | Schäfer, Björn |
| contents | We study C*-algebras generated by two partitions of unity subject to orthogonality relations governed by a bipartite graph which we also call "bipartite graph C*-algebras". These algebras generalize at the same time the C*-algebra $C^\ast(p,q)$ generated by two projections and the hypergraph C*-algebras of Trieb, Weber and Zenner. We describe alternative universal generators of bipartite graph C*-algebras and study partitions of unity in generic position associated to a bipartite graph. As a main result, we prove that bipartite graph C*-algebras are completely classified by their one- and two-dimensional irreducible representations which provides a first step towards a classification of the more general hypergraph C*-algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of Certain C*-Algebras Generated by Two Partitions of Unity Schäfer, Björn Operator Algebras 46L35 (Primary) 46L09, 47C15 (Secondary) We study C*-algebras generated by two partitions of unity subject to orthogonality relations governed by a bipartite graph which we also call "bipartite graph C*-algebras". These algebras generalize at the same time the C*-algebra $C^\ast(p,q)$ generated by two projections and the hypergraph C*-algebras of Trieb, Weber and Zenner. We describe alternative universal generators of bipartite graph C*-algebras and study partitions of unity in generic position associated to a bipartite graph. As a main result, we prove that bipartite graph C*-algebras are completely classified by their one- and two-dimensional irreducible representations which provides a first step towards a classification of the more general hypergraph C*-algebras. |
| title | Classification of Certain C*-Algebras Generated by Two Partitions of Unity |
| topic | Operator Algebras 46L35 (Primary) 46L09, 47C15 (Secondary) |
| url | https://arxiv.org/abs/2509.01309 |