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SUMMARY:Valentin Deaconu (University of Nevada\, Reno)
DTSTART:20201028T190000Z
DTEND:20201028T200000Z
DTSTAMP:20260420T052740Z
UID:NYC-NCG/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/29/"
 >Symmetries of the $C^∗$-algebra of a vector bundle</a>\nby Valentin Dea
 conu (University of Nevada\, Reno) as part of Noncommutative geometry in N
 YC\n\n\nAbstract\nWe consider $C^*$-algebras constructed from compact grou
 p actions  on complex vector bundles $E\\to X$ endowed with a Hermitian me
 tric. An action of $G$   by isometries on $E\\to X$ induces an  action  on
  the $C^*$-correspondence $\\Gamma(E)$  over $C(X)$ consisting of continuo
 us sections\, and on the associated Cuntz-Pimsner algebra $\\mathcal{O}_E$
 \, so we can study the crossed product $\\mathcal{O}_E\\rtimes G$.\n\nIf t
 he action  is free and rank $E=n$\, then we prove that $\\mathcal{O}_E\\rt
 imes G$ is \nMorita-Rieffel equivalent to a field of Cuntz algebras $\\mat
 hcal O_n$ over the orbit space $X/G$.\n\nIf the action   is fiberwise\, th
 en $\\mathcal{O}_E\\rtimes G$ becomes a continuous field of crossed produc
 ts $\\mathcal{O}_n\\rtimes G$. For transitive  actions\, we show that \n$\
 \mathcal{O}_E\\rtimes G$ is Morita-Rieffel equivalent to a graph $C^*$-alg
 ebra.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/29/
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