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SUMMARY:Iason Moutzouris (Purdue University)
DTSTART:20231115T200000Z
DTEND:20231115T210000Z
DTSTAMP:20260420T053338Z
UID:NYC-NCG/142
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/142/
 ">When amenable groups have real rank zero $C^*$-algebras?</a>\nby Iason M
 outzouris (Purdue University) as part of Noncommutative geometry in NYC\n\
 n\nAbstract\nFor every torsion free\, discrete and amenable group $G$\, th
 e Kadison-Kaplansky conjecture has been verified\, so $C^*(G)$ has no nont
 rivial projections. On the other hand\, every torsion element $g\\in G$\, 
 of order $n$\, gives rise to a projection $\\frac{1+g+...+g^{n-1}}{n}\\in 
 C^*(G)$. Actually\, if $G$ is locally finite\, then $C^*(G)$ is an AF-alge
 bra\, so it has an abundance of projections.  So\, it is natural to ask wh
 at happens when the group has both torsion and\nnon-torsion elements. A re
 sult on this direction came from Scarparo\, who showed that for every disc
 rete\, infinite\, finitely generated elementary amenable group\,  $C^*(G)$
  cannot have real rank zero. In this talk\, we will explain why if $G$ is 
 discrete\, amenable and $C^*(G)$ has real rank zero\, then all elementary 
 amenable normal subgroups with finite Hirsch length must be locally finite
 .\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/142/
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