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SUMMARY:Tyrone Crisp (University of Maine)
DTSTART:20210929T190000Z
DTEND:20210929T200000Z
DTSTAMP:20260420T052726Z
UID:NYC-NCG/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/73/"
 >Frobenius C*-algebras and local adjunctions of C*-correspondences</a>\nby
  Tyrone Crisp (University of Maine) as part of Noncommutative geometry in 
 NYC\n\n\nAbstract\nMany interesting and important C*-algebras do not have 
 multiplicative identities\, and C*-algebraists have long known how to deal
  with this fact by using approximate identities\, multiplier algebras\, et
 c. A similar situation arises when one attempts to use methods of category
  theory to study modules over C*-algebras: objects like "the category of c
 ompact operators on Hilbert spaces" don't fit neatly into the standard the
 ory of categories\, because they lack identity morphisms\; but they do fit
  nicely into a theory of non-unital C*-categories and their multiplier cat
 egories\, as developed by Kandelaki\, Mitchener\, Vasselli\, Antoun-Voigt\
 , and others. This talk concerns an adaptation of the important categorica
 l notion of adjoint functors to this non-unital-category point of view. I 
 will present a definition (taken from joint work with Pierre Clare and Nig
 el Higson) of adjoint functors between categories of compact operators on 
 Hilbert C*-modules\, and I will explain how this definition corresponds to
  a natural notion of Frobenius C*-algebra\, mirroring a correspondence bet
 ween two-sided adjunctions and Frobenius algebras in classical category th
 eory.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/73/
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