Lyndon bases of split $ı$quantum groups

Abstract

We introduce and study Lyndon bases of split $ı$quantum groups ${\mathbf{U}}^{ı}(\mathfrak{g})$. A relationship between the Lyndon bases and PBW-type bases was provided. As an application, we establish the existence of canonical bases for the type A split $ı$quantum groups ${\mathbf{U}}^{ı}({\mathfrak{sl}}_n)$.

27 pages; some typos are corrected and some statements are revised