Classification of representations of higher-rank graph C*-algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911601597087744 |
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| author | Brothier, Arnaud Sims, Aidan Wijesena, Dilshan |
| author_facet | Brothier, Arnaud Sims, Aidan Wijesena, Dilshan |
| contents | We develop new techniques for the construction and classification of representations of row-finite and locally convex higher-rank graph C*-algebras O. This class includes Cuntz--Krieger algebras associated to row-finite directed graphs. Our approach relies on the representation theory of a certain non-self-adjoint algebra and a lifting process of representations. We introduce a novel dimension vector for representations of O yielding a countable partition of the spectrum. Given a Cuntz--Krieger algebra and a finite dimension vector, we construct a smooth manifold parametrising the corresponding spectral component. Our techniques are both explicit and functorial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15883 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of representations of higher-rank graph C*-algebras Brothier, Arnaud Sims, Aidan Wijesena, Dilshan Operator Algebras We develop new techniques for the construction and classification of representations of row-finite and locally convex higher-rank graph C*-algebras O. This class includes Cuntz--Krieger algebras associated to row-finite directed graphs. Our approach relies on the representation theory of a certain non-self-adjoint algebra and a lifting process of representations. We introduce a novel dimension vector for representations of O yielding a countable partition of the spectrum. Given a Cuntz--Krieger algebra and a finite dimension vector, we construct a smooth manifold parametrising the corresponding spectral component. Our techniques are both explicit and functorial. |
| title | Classification of representations of higher-rank graph C*-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2604.15883 |