K-theoretic Hall algebras, quantum groups and super quantum groups - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

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

Résumé

We first 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. An essential step consists to deform the K-theoretic Hall algebra so that the deformation is torsion free over some polynomial subalgebra. Next, we compare super toroidal quantum groups of type A with K-theoretic Hall algebras of quivers with potential, which are defined using the Grothendieck groups of categories of singularities of some Landau-Ginzburg models.

Dates et versions

hal-04223862 , version 1 (30-09-2023)

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Michela Varagnolo, Eric Vasserot. K-theoretic Hall algebras, quantum groups and super quantum groups. 2023. ⟨hal-04223862⟩
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