An identification of Lusztig's modified forms of quantum algebras and their analogues

2013/12/03 by Zhaobing Fan, Yiqiang Li, Fan, Zhaobing +1
Mathematics · Physics and Astronomy · #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37

paper · pdf · doi:10.48550/arxiv.1312.0838

arxiv created 2013/12/03 · openalex publication_date 2013/12/03 · arxiv updated 2013/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a multi-parameter twisted Hopf algebra associated with a root datum and show that its modified form is isomorphic to Lusztig's modified quantum algebra under certain restrictions on the parameters. By taking various specializations of the parameters, we obtain similar results for two/multi-parameter quantum algebras and Kang-Kashiwara-Oh's multi-parameter quantum superalgebras. As a consequence, the categories of weight modules of these algebras are identical.

Citations

• Two-parameter quantum algebras, canonical bases and categorifications

Related

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• Multi-parameter Quantum Groups via Quantum Quasi-Symmetric Algebras
• The Lusztig automorphism of the q-Onsager algebra
• Two-parameter quantum algebras, canonical bases and categorifications
• On geometric realizations of quantum modified algebras and their canonical bases, II