Powers averaging for actions on $C(X)$-algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913306624655360 |
|---|---|
| author | Amrutam, Tattwamasi Hirshberg, Ilan Seth, Apurva |
| author_facet | Amrutam, Tattwamasi Hirshberg, Ilan Seth, Apurva |
| contents | Given a unital $C(X)$-algebra $A$ discrete group $Γ$ and an action $α: Γ\to \text{aut}(A)$ which leaves $C(X)$ invariant and such that $C(X)\rtimes_{α,r} Γ$ is simple, and a $2$-cocycle $ω$, we obtain a bijective correspondence between maximal $Γ$-invariant ideals of $A$ and maximal ideals in $A\rtimes_{α,ω,r} Γ$. In particular, $A\rtimes_{α,ω,r} Γ$ is simple if and only if $A$ has no $Γ$-invariant ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07702 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Powers averaging for actions on $C(X)$-algebras Amrutam, Tattwamasi Hirshberg, Ilan Seth, Apurva Operator Algebras Functional Analysis 46L55, 37A55 Given a unital $C(X)$-algebra $A$ discrete group $Γ$ and an action $α: Γ\to \text{aut}(A)$ which leaves $C(X)$ invariant and such that $C(X)\rtimes_{α,r} Γ$ is simple, and a $2$-cocycle $ω$, we obtain a bijective correspondence between maximal $Γ$-invariant ideals of $A$ and maximal ideals in $A\rtimes_{α,ω,r} Γ$. In particular, $A\rtimes_{α,ω,r} Γ$ is simple if and only if $A$ has no $Γ$-invariant ideals. |
| title | Powers averaging for actions on $C(X)$-algebras |
| topic | Operator Algebras Functional Analysis 46L55, 37A55 |
| url | https://arxiv.org/abs/2312.07702 |