Compactification of quasi-local algebras on the lattice
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914300120006656 |
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| author | Ikeda, Jun |
| author_facet | Ikeda, Jun |
| contents | We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the construction recovers Ocneanu's Tube algebra for fusion spin chains, and provides a canonical bridge between infinite-volume observables and observables with periodic boundary conditions. We exploit this connection to derive an obstruction for the implementability of such topological symmetries as Kramers-Wannier type dualities on symmetric subalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compactification of quasi-local algebras on the lattice Ikeda, Jun Mathematical Physics Operator Algebras Quantum Algebra 46N50 (Primary) 81T45 (Secondary) We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the construction recovers Ocneanu's Tube algebra for fusion spin chains, and provides a canonical bridge between infinite-volume observables and observables with periodic boundary conditions. We exploit this connection to derive an obstruction for the implementability of such topological symmetries as Kramers-Wannier type dualities on symmetric subalgebras. |
| title | Compactification of quasi-local algebras on the lattice |
| topic | Mathematical Physics Operator Algebras Quantum Algebra 46N50 (Primary) 81T45 (Secondary) |
| url | https://arxiv.org/abs/2510.18021 |