On Diagonal bimodules of étale groupoid $C^*$-algebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918216201142272 |
|---|---|
| author | Liu, Rui Qiang, Xiangqi Hou, Chengjun |
| author_facet | Liu, Rui Qiang, Xiangqi Hou, Chengjun |
| contents | We study diagonal bimodules of étale groupoid $C^*$-algebras over their canonical diagonal subalgebras, and establish necessary and sufficient conditions for such a bimodule to be spectral-that is, determined by its spectrum. For a class of $Γ$-graded étale groupoids, we prove that the spectrality of diagonal bimodules is equivalent to their invariance under the action of the dual group $\widehatΓ$ in the abelian case, or under the coaction of $Γ$ in the nonabelian case, on the groupoid $C^*$-algebras, both of which are induced by the underlying cocycle. This framework covers transformation groupoids arising from homeomorphism actions of countable groups, as well as from local homeomorphism actions of Ore semigroups. As applications, we characterize the spectrality of closed two-sided ideals and subalgebras that contain the diagonal subalgebra of étale groupoid $C^*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Diagonal bimodules of étale groupoid $C^*$-algebras Liu, Rui Qiang, Xiangqi Hou, Chengjun Operator Algebras We study diagonal bimodules of étale groupoid $C^*$-algebras over their canonical diagonal subalgebras, and establish necessary and sufficient conditions for such a bimodule to be spectral-that is, determined by its spectrum. For a class of $Γ$-graded étale groupoids, we prove that the spectrality of diagonal bimodules is equivalent to their invariance under the action of the dual group $\widehatΓ$ in the abelian case, or under the coaction of $Γ$ in the nonabelian case, on the groupoid $C^*$-algebras, both of which are induced by the underlying cocycle. This framework covers transformation groupoids arising from homeomorphism actions of countable groups, as well as from local homeomorphism actions of Ore semigroups. As applications, we characterize the spectrality of closed two-sided ideals and subalgebras that contain the diagonal subalgebra of étale groupoid $C^*$-algebras. |
| title | On Diagonal bimodules of étale groupoid $C^*$-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2511.18459 |