Yangians from cohomological Hall algebras

          @misc{ scivideos_PIRSA:19020057,
            doi = {10.48660/19020057},
            url = {https://pirsa.org/19020057},
            author = {Davison, Ben},
            keywords = {Mathematical physics},
            language = {en},
            title = {Yangians from cohomological Hall algebras},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020057 see, \url{https://scivideos.org/index.php/pirsa/19020057}}
          }
          

Abstract

I will explain various features of the preprojective CoHA, a kind of universal algebra of correspondences generalising the algebras of endomorphisms of cohomology of quiver varieties considered by Nakajima. In particular I will focus on features of this algebra that become visible after viewing it as a dimensional reduction of the Kontsevich-Soibelman) critical CoHA associated to a related 3-dimensional Calabi-Yau category. Many nice features emerge from this view, e.g. an embedding in a related shuffle algebra, a formula for the graded dimension of the algebra, a flat non cocommutative deformation, a cocommutative coproduct, a geometric doubling procedure, the PBW theorem, an isomorphism with the Yangian considered by Maulik and Okounkov... I will focus on the perverse filtration, which is the key feature of my joint work with Sven Meinhardt, and gives rise to most of the above