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When the reduced twisted $C^*$-algebra $C^*_r(\mathcal{G}, c)$ of a non-principal groupoid $\mathcal{G}$ admits a Cartan subalgebra, Renault's work on Cartan subalgebras implies the existence of another groupoid description of $C^*_r(\mathcal{G}, c)$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7633506f6755eeefcd49ba6ce853747a
https://lirias.kuleuven.be/handle/20.500.12942/713230
https://lirias.kuleuven.be/handle/20.500.12942/713230
Autor:
Heath Emerson, Anna Duwenig
Publikováno v:
Transactions of the American Mathematical Society, Series B. 7:254-289
An early result of Noncommutative Geometry was Connes' observation in the 1980's that the Dirac-Dolbeault cycle for the $2$-torus $\mathbb{T}^2$, which induces a Poincar\'e self-duality for $\mathbb{T}^2$, can be 'quantized' to give a spectral triple
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b029fb254b9875324c0c0dd2fe7b2eff
https://doi.org/10.1090/btran/54
https://doi.org/10.1090/btran/54
Publikováno v:
Journal of Mathematical Analysis and Applications. 516:126530
If $p \colon \mathcal B\to G$ is a Fell bundle over an \'etale groupoid, then we show that there is an norm reducing injective linear map $j \colon C^*_r(G;\mathcal B)\to \Gamma_{0}(G;\mathcal B)$ generalizing the well know map $j \colon C^*_{r}(G)\t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45f8297c343a26e241b3958e3874f703
https://doi.org/10.1016/j.jmaa.2022.126530
https://doi.org/10.1016/j.jmaa.2022.126530
Autor:
Anna Duwenig
Publikováno v:
Rocky Mountain J. Math. 50, no. 1 (2020), 91-124
If a differential operator $D$ on a smooth Hermitian vector bundle $S$ over a compact manifold $M$ is symmetric, it is essentially self-adjoint and so admits the use of functional calculus. If $D$ is also elliptic, then the Hilbert space of square in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::73009b140d2afc952083245e37cb8ed0
https://doi.org/10.1216/rmj.2020.50.91
https://doi.org/10.1216/rmj.2020.50.91
Renault proved in 2008 that if $G$ is a topologically principal groupoid, then $C_0(G^{(0)})$ is a Cartan subalgebra in $C^*_r(G, \Sigma)$ for any twist $\Sigma$ over $G$. However, there are many groupoids which are not topologically principal, yet t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::399dafd5aff26c33ae2a9c55bca42e00
http://arxiv.org/abs/2001.08270
http://arxiv.org/abs/2001.08270
Autor:
Boyu Li, Anna Duwenig
Publikováno v:
Journal of Functional Analysis. 282:109268
We define the Zappa-Sz\'{e}p product of a Fell bundle by a groupoid, which turns out to be a Fell bundle over the Zappa-Sz\'{e}p product of the underlying groupoids. Under certain assumptions, every Fell bundle over the Zappa-Sz\'{e}p product of grou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5ff00ad9519003eaf6c84399b27242c9
https://doi.org/10.1016/j.jfa.2021.109268
https://doi.org/10.1016/j.jfa.2021.109268