Tuesday, January 14, 15:15, 7.527
Andrea Pasquali, Triangulations on orbifold surfaces and skew group algebras.
Cluster algebras arising from surface triangulations are by now a
classical and rich theory. It makes sense to study how far this theory can
be extended to surfaces with some singularities, for instance orbifold
points. In a recent paper, Amiot and Plamondon opened the way by
convincingly interpreting the "punctures" of classical cluster algebras from
surfaces as "orbifold points of order 2". The connection between the
corresponding Jacobian algebras is then given by a skew group algebra
construction. Motivated by this, I will speak about skew group algebras of
Jacobian algebras in general, explaining what is known and what is
difficult. This will hopefully shed some light on the broader problem of
constructing algebras from triangulations of orbifold surfaces.