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SUMMARY:Lang Mou (Cambridge)
DTSTART:20220426T140000Z
DTEND:20220426T150000Z
DTSTAMP:20260423T005734Z
UID:TRAC/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TRAC/46/">Lo
 cally free Caldero-Chapoton functions for rank 2 cluster algebras</a>\nby 
 Lang Mou (Cambridge) as part of The TRAC Seminar - Théorie de Représenta
 tions et ses Applications et Connections\n\n\nAbstract\nAssociated to any 
 acyclic skew-symmetrizable matrix B and a symmetrizer\, Geiss\, Leclerc an
 d Schröer have defined a finite-dimensional algebra H over any field. Man
 y geometric constructions for acyclic quivers carry over to this situation
  by using complex numbers. They show that in finite types\, the non-initia
 l cluster variables (of the cluster algebra associated to B) are exactly t
 he locally free Caldero—Chapoton functions of indecomposable locally fre
 e rigid H-modules and conjecture it to be true in general. We verify this 
 conjecture in rank 2 by showing that the locally free F-polynomials of cer
 tain modules under reflection functors satisfy the same recursion of the F
 -polynomials of cluster variables. This is joint work with Daniel Labardin
 i-Fragoso.\n
LOCATION:https://researchseminars.org/talk/TRAC/46/
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