BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Trey Trampel (University of Notre Dame)
DTSTART:20210323T150000Z
DTEND:20210323T160000Z
DTSTAMP:20260423T021137Z
UID:OCAS/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OCAS/23/">Ro
 ot of unity quantum cluster algebras and discriminants</a>\nby Trey Trampe
 l (University of Notre Dame) as part of Online Cluster Algebra Seminar (OC
 AS)\n\n\nAbstract\nWe will define the notion of a root of unity quantum cl
 uster algebra\, which is not necessarily a specialization of a quantum clu
 ster algebra. Through these algebras\, we connect the subjects of cluster 
 algebras and discriminants. Motivation for discriminants will be given in 
 terms of their applications to representation theory. We show that the roo
 t of unity quantum cluster algebras are polynomial identity algebras\, and
  we identify a large canonical central subalgebra. This central subalgebra
  is shown to be isomorphic to the underlying classical cluster algebra of 
 geometric type. These central subalgebras can be thought of as a generaliz
 ation of De Concini-Kac-Procesi's canonical central subalgebras for quantu
 m groups at roots of unity. In particular\, we recover their structure in 
 the case of quantum Schubert cells. We prove a general theorem on the form
  of discriminants\, which is given as a product of frozen cluster variable
 s. From this we derive specific formulas in examples\, such as for all roo
 t of unity quantum Schubert cells for any symmetrizable Kac-Moody algebra.
  This is joint work with Bach Nguyen and Milen Yakimov.\n
LOCATION:https://researchseminars.org/talk/OCAS/23/
END:VEVENT
END:VCALENDAR