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SUMMARY:Chris Bruce (Queen Mary University of London and the University of
  Glasgow)
DTSTART:20201130T160000Z
DTEND:20201130T170000Z
DTSTAMP:20260423T035931Z
UID:GOBA/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOBA/10/">C*
 -algebras from actions of congruence monoids</a>\nby Chris Bruce (Queen Ma
 ry University of London and the University of Glasgow) as part of Groups\,
  Operators\, and Banach Algebras Webinar\n\n\nAbstract\nI will give an ove
 rview of recent results for semigroup C*-algebras associated with number f
 ields. These results are already interesting in the case where the field i
 s the rational numbers\, and I will focus mostly on this case to make ever
 ything more explicit and accessible.\nC*-algebras of full ax+b-semigroups 
 over rings of algebraic integers were first studied by Cuntz\, Deninger\, 
 and Laca\; their construction has since been generalized by considering ac
 tions of congruence monoids. Semigroup C*-algebras obtained this way provi
 de an example class of unital\, separable\, nuclear\, strongly purely infi
 nite C*-algebras which\, in many cases\, completely characterize the initi
 al number-theoretic data. They also carry canonical time evolutions\, and 
 the associated C*-dynamical systems exhibit intriguing phenomena. For inst
 ance\, the striking similarity between the K-theory formula and the parame
 terization space for the low temperature KMS states\, observed by Cuntz in
  the case of the full ax+b-semigroup\, persists in the more general settin
 g.\nPart of this work is joint with Xin Li\, and part is joint with Marcel
 o Laca and Takuya Takeishi.\n
LOCATION:https://researchseminars.org/talk/GOBA/10/
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