K-theoretic Hall algebras, quantum groups and super quantum groups

M. Varagnolo ^[1] ; E. Vasserot ^[2]
1. [1] CY Cergy Paris Université, Francia
2. [2] Université de Paris, Francia
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 1, 2022
Idioma: inglés
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Resumen
- We prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. We also compare super toroidal quantum groups of type A with some K-theoretic Hall algebras of quivers with potential introduced recently by Padurariu using categories of singularities of some Landau–Ginzburg models. The proof uses both a deformation of the K-theoretic Hall algebra and a dimensional reduction which allows us to compare the KHA of preprojective algebras to the K-theoretic Hall algebras of a quiver with potential.