Hall algebras and quantum symmetric pairs of Kac-Moody type

Abstract

We extend our $ı$Hall algebra construction from acyclic to arbitrary $ı$quivers, where the $ı$quiver algebras are infinite-dimensional 1-Gorenstein in general. Then we establish an injective homomorphism from the universal $ı$quantum group of Kac-Moody type arising from quantum symmetric pairs to the $ı$Hall algebra associated to a virtually acyclic $ı$quiver.

v2, 41 pages, a Hall multiplication formula added in Proposition 3.10, and used to simplify proof of Proposition 7.3

References in corpus (6)

• Quantum symmetric Kac-Moody pairs
• The half-infinite XXZ chain in Onsager's approach
• Canonical bases for tensor products and super Kazhdan-Lusztig theory
• Quivers with relations for symmetrizable Cartan matrices I : Foundations
• Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
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Cited by in corpus (3)

• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
• Relative braid group symmetries on $ı$quantum groups of Kac-Moody type
• Braid group action and quasi-split affine $ı$quantum groups I