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arXiv · 2011.01203

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

Michela Varagnolo·Eric Vasserot
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Abstract

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.

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Michela Varagnolo, Eric Vasserot. 2020-11-02. K-theoretic Hall algebras, quantum groups and super quantum groups. https://arxiv.org/abs/2011.01203

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