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

2020/11/02 by Varagnolo, Michela, Vasserot, Eric · 4 citations
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2011.01203

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.

Cited by

• 0-affine quantum groups as K-theoretic Hall algebras
• Kleinian orbifolds, Cohomological Hall Algebras, and Yangians
• Abelian Hall categories
• Comparison of Cohomological and K-theoretical Hall algebra

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