Bases of quantized enveloping algebras

Bangming Deng and Jie Du

Vol. 220 (2005), No. 1, 33–48

DOI: 10.2140/pjm.2005.220.33

Abstract

We give a systematic description of many monomial bases for a specified quantized enveloping algebra and of many integral monomial bases for the associated Lusztig ℤ[v,v⁻¹]-form. The relations among monomial bases, PBW bases and canonical bases are also discussed.

Keywords

quantized enveloping algebra, Ringel–Hall algebra, generic extension, monomial basis, canonical basis

Mathematical Subject Classification 2000

Primary: 17B37, 16G20

Milestones

Received: 15 August 2003

Revised: 10 June 2004

Accepted: 10 June 2004

Published: 1 May 2005