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SUMMARY:Aidan Sims (Wollongong)
DTSTART:20200702T100000Z
DTEND:20200702T110000Z
DTSTAMP:20260419T055742Z
UID:CRMDS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRMDS/7/">Gr
 aded K-theory for Z_2-graded graph C*-algebras</a>\nby Aidan Sims (Wollong
 ong) as part of Western Sydney University Abend Seminars\n\n\nAbstract\nWh
 ile there is no universally agreed-upon definition of Z_2-graded K-theory 
 for C*-algebras\, a very natural way to define it is using Kasparov's cele
 brated KK-bifunctor: KK is naturally a Z_2-graded theory\, and Kasparov pr
 oved that if applied to trivially-graded C*-algebras A\, the groups KK_*(\
 \mathbb{C}\, A) are the K-groups of A. So it is natural to define K^{gr}_*
 (A) as KK_*(\\mathbb{C}\, A) for Z_2-graded C*-algebras A in general. I wi
 ll discuss recent work with Adam Sierakowski and with honours students Qui
 nn Patterson and Jonathan Taylor\, building on previous work with Kumjian 
 and Pask\, that uses deep ideas of Pimsner to compute the graded K-theory\
 , defined in this way\, of relative graph C*-algebras carrying Z_2-grading
 s determined by binary labellings of the edges of the graph: the formulas 
 that emerge strongly suggest that this notion of graded K-theory captures 
 the right sort of information.\n
LOCATION:https://researchseminars.org/talk/CRMDS/7/
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