Invariant measures on the transversal hull of cone semigroups and some applications
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| Format: | Preprint |
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2025
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| _version_ | 1866908442047807488 |
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| author | Ojito, Danilo Polo Prodan, Emil Stoiber, Tom |
| author_facet | Ojito, Danilo Polo Prodan, Emil Stoiber, Tom |
| contents | Let $\LL_{\bf v}\subset \Z^D$ be a suitable cone semigroup and $\A_{\bf v}$ its reduced semigroup $C^*$-algebra. In this paper, we compute the $\LL_{\bf v}$-invariant measures in the transversal hull of the semigroup $\LL_{\bf v}$ that exhibit regularity in the boundaries of $\LL_{\bf v}.$ These measures enable the construction of a trace per-unit hypersurface for observables in $\A_{\bf v}$ supported near the boundaries of $\LL_{\bf v}$, leading to the construction of appropriate Chern cocycles in the "boundary" ideals of $\A_{\bf v}$. Our approach applies to both finitely and non-finitely generated cone semigroups. Applications for the bulk-defect correspondence of lattice models of topological insulators are also provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_06757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariant measures on the transversal hull of cone semigroups and some applications Ojito, Danilo Polo Prodan, Emil Stoiber, Tom Mathematical Physics Operator Algebras Let $\LL_{\bf v}\subset \Z^D$ be a suitable cone semigroup and $\A_{\bf v}$ its reduced semigroup $C^*$-algebra. In this paper, we compute the $\LL_{\bf v}$-invariant measures in the transversal hull of the semigroup $\LL_{\bf v}$ that exhibit regularity in the boundaries of $\LL_{\bf v}.$ These measures enable the construction of a trace per-unit hypersurface for observables in $\A_{\bf v}$ supported near the boundaries of $\LL_{\bf v}$, leading to the construction of appropriate Chern cocycles in the "boundary" ideals of $\A_{\bf v}$. Our approach applies to both finitely and non-finitely generated cone semigroups. Applications for the bulk-defect correspondence of lattice models of topological insulators are also provided. |
| title | Invariant measures on the transversal hull of cone semigroups and some applications |
| topic | Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2507.06757 |