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SUMMARY:Pere Ara (Barcelona)
DTSTART:20200625T100000Z
DTEND:20200625T110000Z
DTSTAMP:20260419T060342Z
UID:CRMDS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRMDS/10/">G
 raded K-Theory\, Filtered K-theory and the classification of graph algebra
 s</a>\nby Pere Ara (Barcelona) as part of Western Sydney University Abend 
 Seminars\n\n\nAbstract\nWe prove that an isomorphism of  graded Grothendie
 ck groups of two Leavitt path algebras  induces an isomorphism of a certai
 n quotient of algebraic filtered K-theory and consequently an isomorphism 
 of filtered K-theory of their associated graph C*-algebras. As an applicat
 ion\, we show that\, since for a finite graph E with no sinks\, the graded
  Grothendieck group of L(E) coincides with Krieger's dimension group of it
 s adjacency matrix\, our result relates the shift equivalence of graphs to
  the filtered K-theory and consequently gives that two arbitrary shift equ
 ivalent matrices give stably isomorphic graph C*-algebras. This result was
  only known for irreducible graphs. This is a joint work with Roozbeh Hazr
 at and Huanhuan Li\n
LOCATION:https://researchseminars.org/talk/CRMDS/10/
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