Canonical bases arising from quantized enveloping algebras

TLDR

A class of bases for U+ was previously constructed by D. Lusztig. The study aims to construct bases of U+ over Q(v). The authors modify PBW‑type bases that specialize to Poincaré–Birkhoff–Witt bases when v = 1.

Abstract

0.2. We are interested in the problem of constructing bases of U+ as a Q(v) vector space. One class of bases of U+ has been given in [DL]. We call them (or, rather, a slight modification of them, see ?2) bases of PBW type, since for v = 1, they specialize to bases of U+ of the type provided by the Poincare see however ? 12.)