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SUMMARY:Joeri De Ro (IMPAN\, Poland)
DTSTART:20251110T150000Z
DTEND:20251110T160000Z
DTSTAMP:20260422T181313Z
UID:QGS/133
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/133/">Eq
 uivariant Eilenberg-Watts theorems for locally compact quantum groups</a>\
 nby Joeri De Ro (IMPAN\, Poland) as part of Quantum Groups Seminar [QGS]\n
 \n\nAbstract\nGiven actions of a locally compact quantum group $G$ on the 
 von Neumann algebras $A$ and $B$\, we can associate to it the category $\\
 operatorname{Corr}^G(A\,B)$ of G-A-B-correspondences. Special cases of thi
 s category include the category $\\operatorname{Rep}(A)$ of unital\, norma
 l $*$-representations of $A$ on Hilbert spaces and the category $\\operato
 rname{Rep}^G(A)$ of unital\, normal\, $G$-representations on Hilbert space
 s. We construct actions $\\operatorname{Rep}^G(A)\\curvearrowleft \\operat
 orname{Rep}(G)$ and $\\operatorname{Rep}(A)\\curvearrowleft \\operatorname
 {Rep}(\\hat{G})$\, providing us with natural examples of module categories
 . We show that the categories of module functors $\\operatorname{Rep}(B)\\
 to \\operatorname{Rep}(A)$ and \n$\\operatorname{Rep}^G(B)\\to \\operatorn
 ame{Rep}^G(A)$ are both equivalent to the category of $G$-$A$-$B$-correspo
 ndences\, providing equivariant versions of the von Neumann algebraic Eile
 nberg-Watts theorem.\n
LOCATION:https://researchseminars.org/talk/QGS/133/
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