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SUMMARY:Spanier-Whitehead K-Duality and Duality of Extensions of C*-algebr
 as - Ulrich Pennig (Cardiff University)
DTSTART:20250704T130000Z
DTEND:20250704T133000Z
UID:TALK233218@talks.cam.ac.uk
DESCRIPTION:The stable homotopy category of topological spaces comes with 
 a notion of duality\, called Spanier-Whitehead duality. The KK-groups of C
 *-algebras form the morphisms in a triangulated category that is in many a
 spects the operator algebraic analogue of the stable homotopy category. It
  is straightforward to transfer the definition of duality to KK-theory. In
  joint work with Taro Sogabe we showed that this duality is compatible wit
 h the triangulated structure. As an application we study duality of extens
 ions in the sense of Matsumoto. We were able to show that any extension of
  a separable unital nuclear UCT C*-algebra with finitely generated K-group
 s by the compact operators has a strongly K-theoretic dual. In the special
  case of Cuntz-Krieger algebras the dual of the Toeplitz extension is the 
 Cuntz-Krieger algebra associated to the transposed matrix.&nbsp\;
LOCATION:External
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