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SUMMARY:Damián Ferraro (Departamento de Matemática y Estadística del Li
 toral\, Uruguay)
DTSTART:20240207T200000Z
DTEND:20240207T210000Z
DTSTAMP:20260420T053205Z
UID:NYC-NCG/150
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/150/
 ">Cross-sectional C*-algebras of Fell bundles</a>\nby Damián Ferraro (Dep
 artamento de Matemática y Estadística del Litoral\, Uruguay) as part of 
 Noncommutative geometry in NYC\n\n\nAbstract\nA Fell bundle (or C*-algebra
 ic bundle) $B=\\{B_t\\}_{t\\in G}$ may be thought of as a kind of action o
 f the base group $G$ on the C*-algebra $B_e$\, $e$ being the unit of $G.$ 
 When doing so\, the full and reduced cross-sectional C*-algebras of $B$\, 
 $C^*(B)$ and $C^*_r(B)$ respectively\, become the full and reduced crossed
  products of the action.\n\nIt is implicit in Exel-Ng's construction/chara
 cterization of $C^*_r(B)$ that the induction of representations from $H:=\
 \{e\\}$ to $G\,$ $U\\mapsto Ind_{H\\uparrow G}(U)\,$ and from $B_e$ to $B\
 ,$ $T\\mapsto Ind_{B_e\\uparrow B}(T)\,$ are intimately related and that b
 oth can be used to define/describe $C^*_r(B).$ If $B$ is saturated\, the e
 quivalence of the definitions is a straightforward consequence of Fell's a
 bsorption principle.\n\nThe situation is not so clear when one considers c
 losed subgroups $H$ of $G$ other than $\\{e\\}$ (even if $B$ is saturated)
 .\nThe reduction of $B$ to $H\,$ $B_H:=\\{B_t\\}_{t\\in H}\,$ is a Fell bu
 ndle and one has induction processes $U\\mapsto Ind_{H\\uparrow G}(U)$ and
  $T\\mapsto Ind_{B_H\\uparrow B}(T)\,$ where $U$ and $T$ stand for represe
 ntations of $H$ and $B_H\,$ respectively. In this talk we use $U\\mapsto I
 nd_{H\\uparrow G}(U)$ and $T\\mapsto Ind_{B_H\\uparrow B}(T)$ to construct
  two candidates for the "reduced $H$-cross-sectional C*-algebra of $B$". W
 e also give conditions implying they are isomorphic.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/150/
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