On bases of quantized enveloping algebras

2003/07/18 by Bangming Deng, Jie Du, Deng, Bangming +1
Mathematics · Physics and Astronomy · #16G20 #17B37 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16G20 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0307258

13 pages

arxiv created 2003/07/18 · openalex publication_date 2003/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Monomial Bases of Quantized Enveloping Algebras
• Canonical bases of the modified quantized enveloping algebras of type A₂
• History of the canonical basis and crystal basis
• Dual Standard Monomial Theoretic Basis and Canonical Basis for Type A
• The Lusztig cones of a quantized enveloping algebra of type A