Tracial weights on topological graph algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929596787589120 |
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| author | Christensen, Johannes |
| author_facet | Christensen, Johannes |
| contents | We describe two kinds of regular invariant measures on the boundary path space of a second countable topological graph, which allows us to describe all extremal tracial weights on the graph C$^{*}$-algebra which are not gauge-invariant. Using this description we prove that all tracial weights on the C$^{*}$-algebra of a second countable topological graph are gauge-invariant when the graph is free. This in particular implies that all tracial weights are gauge-invariant when the graph C$^{*}$-algebra is simple and separable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12122 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tracial weights on topological graph algebras Christensen, Johannes Operator Algebras We describe two kinds of regular invariant measures on the boundary path space of a second countable topological graph, which allows us to describe all extremal tracial weights on the graph C$^{*}$-algebra which are not gauge-invariant. Using this description we prove that all tracial weights on the C$^{*}$-algebra of a second countable topological graph are gauge-invariant when the graph is free. This in particular implies that all tracial weights are gauge-invariant when the graph C$^{*}$-algebra is simple and separable. |
| title | Tracial weights on topological graph algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2208.12122 |