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SUMMARY:Laurent Cantier (Universitat Autònoma de Barcelona)
DTSTART:20210908T190000Z
DTEND:20210908T200000Z
DTSTAMP:20260420T053205Z
UID:NYC-NCG/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/66/"
 >Classification of unitary elements of a C*-algebra</a>\nby Laurent Cantie
 r (Universitat Autònoma de Barcelona) as part of Noncommutative geometry 
 in NYC\n\n\nAbstract\nThe Cuntz semigroup has emerged as an essential tool
  for the classification of (non-simple) C*-algebras. For instance\, it has
  been shown that the functor Cu classifies positive elements of any C*-alg
 ebra of stable rank 1 (up to approximately unitarily equivalence). An imme
 diate corollary is that the Cuntz semigroup is a complete invariant for AI
  algebras. In this talk\, I will raise the question of classification of u
 nitary elements of a C*-algebra (of stable rank 1). It is unlikely that th
 e Cuntz semigroup alone is sufficient to classify these elements and one c
 an speculate that an ingredient with $K_1$ flavor has to be added. Neverth
 eless\, I will prove that this remains true when restricting to AF algebra
 s and I will discuss how one could to extend this classification result to
  a larger class of C*-algebra.\n\nEven though I will recall definitions of
  the Cuntz semigroup and classifying functor\, it might good to point out 
 that knowledge about C*-algebras are needed.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/66/
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