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SUMMARY:Peigen Cao (Hebrew University)
DTSTART:20220411T120000Z
DTEND:20220411T130000Z
DTSTAMP:20260710T081342Z
UID:paris-algebra-seminar/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paris-algebr
 a-seminar/90/">On exchange matrices from string diagrams</a>\nby Peigen Ca
 o (Hebrew University) as part of Paris algebra seminar\n\nLecture held in 
 Zoom.\n\nAbstract\nIn this talk\, we will first recall the constructions o
 f triangular extension and of source-sink extensio for skew-symmetrizable 
 matrices and some invariants under these constructions. Secondly\, we will
  recall the string diagrams introduced by Shen-Weng\, which are very usefu
 l to describe many interesting skew-symmetrizable matrices closely related
  with Lie theory. Thirdly\, we will sketch the proof of our main result: t
 he skew-symmetrizable matrices from string diagrams are in the smallest cl
 ass of skew-symmetrizable matrices containing the (1 times 1) zero matrix 
 and closed under mutations and source-sink extensions. This result applies
  to the exchange matrices of cluster algebras from double Bruhat cells\, u
 nipotent cells\, double Bott-Samelson cells among others. Finally\, some i
 mmediate applications regarding reddening sequences and non-degenerate pot
 entials for many quivers from Lie theory are given.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/90/
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