Non-symmetrizable quantum groups: defining ideals and specialization

TL;DR

This paper introduces new generating sets for the defining ideal of Nichols algebras of diagonal type and applies them to analyze the bar involution and specialization issues in non-symmetrizable quantum groups.

Contribution

It provides novel generating sets for Nichols algebra ideals and advances understanding of bar involution and specialization in non-symmetrizable quantum groups.

Findings

New generating sets for Nichols algebra ideals are established.

The study offers insights into the bar involution in non-symmetrizable quantum groups.

Results contribute to the understanding of specialization problems in these quantum groups.

Abstract

Two generating sets of the defining ideal of a Nichols algebra of diagonal type are proposed, which are then applied to study the bar involution and the specialization problem of quantum groups associated to non-symmetrizable generalized Cartan matrices.