PIRSA:20060040

K-theoretic Hall algebras for quivers with potential

Padurariu, T. (2020). K-theoretic Hall algebras for quivers with potential. Perimeter Institute. https://pirsa.org/20060040

Padurariu, Tudor. K-theoretic Hall algebras for quivers with potential. Perimeter Institute, Jun. 23, 2020, https://pirsa.org/20060040 

          @misc{ pirsa_PIRSA:20060040,
            doi = {10.48660/20060040},
            url = {https://pirsa.org/20060040},
            author = {Padurariu, Tudor},
            keywords = {Mathematical physics},
            language = {en},
            title = {K-theoretic Hall algebras for quivers with potential},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {jun},
            note = {PIRSA:20060040 see, \url{https://pirsa.org}}
          }

Tudor Padurariu

Massachusetts Institute of Technology (MIT)

Talk number
PIRSA:20060040
Collection
Talk Type
Subject
Abstract
Given a quiver with potential, Kontsevich-Soibelman 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 Maulik-Okounkov. For general (Q,W), the Hall algebra has nice structure properties, for example Davison-Meinhardt proved a PBW theorem for it using the decomposition theorem. One can define a K-theoretic 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 K-theory, replacing the use of the decomposition theorem with semi-orthogonal decompositions.