University of Connecticut

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Algebra Seminar
Frieze varieties: A characterization of the finite-tame-wild trichotomy for acyclic quivers
Ralf Schiffler (University of Connecticut)

Wednesday, January 30, 2019
11:15am – 12:05pm

Storrs Campus
Monteith, 313

Given a quiver (=oriented graph) without oriented cycles, one can construct its frieze variety. It is defined in an elementary recursive way by constructing a set of points in affine space. From a more conceptual viewpoint, the coordinates of these points are specializations of cluster variables in the cluster algebra associated to the quiver. We give a new characterization of the finite--tame--wild trichotomy for acyclic quivers in terms of their frieze varieties. We show that an acyclic quiver is representation finite, tame, or wild, respectively, if and only if the dimension of its frieze variety is 0,1 or >1, respectively. This is a joint work with Lee, Li, Mills and Seceleanu

Contact:

Mihai Fulger, mihai.fulger@uconn.edu

Algebra Seminar (primary), UConn Master Calendar

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