Hall algebras and quantum symmetric pairs of Kac-Moody type II

TL;DR

This paper extends the realization of $ extit{i}$Hall algebras for $ extit{i}$quantum groups from quantum symmetric pairs of Kac-Moody type, broadening the scope to arbitrary $ extit{i}$quivers beyond previous restrictions.

Contribution

It generalizes the $ extit{i}$Hall algebra realization to include arbitrary $ extit{i}$quivers, not limited to virtually acyclic cases, establishing a broader framework.

Findings

Established an injective homomorphism for universal $ extit{i}$quantum groups

Extended the realization to arbitrary $ extit{i}$quivers

Generalized previous results by Lu-Wang

Abstract

We extend the $\imath$Hall algebra realization of $\imath$quantum groups arising from quantum symmetric pairs, which establishes an injective homomorphism from the universal $\imath$quantum group of Kac-Moody type to the $\imath$Hall algebra associated to an arbitrary $\imath$quiver (not necessarily virtually acyclic). This generalizes Lu-Wang's result.