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 (2)

• Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
• Teichmüller Theory of Bordered Surfaces

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