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

Eric Vasserot; Michela Varagnolo

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

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arxiv 2011.01203 v5 pith:KBHQU7LF submitted 2020-11-02 math.RT math.QA

Michela Varagnolo , Eric Vasserot This is my paper · ORCID

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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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Hall induction for cotangent representations and wheel conditions
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For cotangent representations of reductive groups with a suitable torus, Borel-Moore homology of the zero fiber is torsion free and the K-theoretic restriction satisfies wheel-type ideal divisibility conditions.

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