Ktheoretic Hall algebras for quivers with potential Speaker(s): Tudor Padurariu
Abstract: Given a quiver with potential, KontsevichSoibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q,W). In particular cases, one recovers positive parts of Yangians as defined by MaulikOkounkov. For general (Q,W), the Hall algebra has nice structure properties, for example DavisonMeinhardt proved a PBW theorem for it using the decomposition theorem.
One can define a Ktheoretic version of this algebra using certain categories of singularities that depend on the stack of
representations of (Q,W). In particular cases, these Hall algebras are positive parts of quantum affine algebras. We show that some of the structure properties in cohomology, such as the PBW theorem, can be lifted to Ktheory, replacing the use of the decomposition theorem with semiorthogonal decompositions.
Date: 23/06/2020  3:15 pm
Collection: Geometric Representation Theory
