K-theoretic Hall algebras, quantum groups and super quantum groups
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...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2011.01203 |