Analogue of Feigin's map on $\imath$quantum group of split type

TL;DR

This paper constructs an algebra homomorphism from the universal $ extit{ extbf{i}}$quantum group of split type to a quantum torus, extending Feigin's map to the $ extit{ extbf{i}}$quantum group setting, broadening the understanding of their algebraic structure.

Contribution

It introduces an $ extit{ extbf{i}}$analogue of Feigin's map for split type $ extit{f i}$quantum groups, establishing a new algebraic connection to quantum tori.

Findings

Established an algebra homomorphism for split type $ extit{f i}$quantum groups.

Extended Feigin's map to the $ extit{f i}$quantum group context.

Provided a new perspective on the algebraic structure of $ extit{f i}$quantum groups.

Abstract

The (universal) $\imath$quantum groups are as a vast generalization of (Drinfeld double) quantum groups. We establish an algebra homomorphism from universal $\imath$quantum group of split type to a certain quantum torus, which can be viewed as an $\imath$analogue of Feigin's map on the quantum group.