Derivations of the two-parameter quantized enveloping algebra \U

2011/06/09 by Xin Tang, Tang, Xin · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.1106.1907

arxiv created 2011/06/09 · openalex publication_date 2011/06/09 · arxiv updated 2011/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let r,s be two parameters chosen from \C^∗ such that r^msⁿ=1 implies m=n=0. We compute the derivations of the two-parameter quantized enveloping algebra \U and calculate its first degree Hochschild cohomology group. We further determine the group of algebra automorphisms for the two-parameter Hopf algebra \V. As a result, we determine the group of Hopf algebra automorphisms for \V.

Cited by

• Simple Modules and PI Structure of the Two-Parameter Quantized Algebra U⁺_r,s(B₂)
• Derivations and Hochschild cohomology of quantum nilpotent algebras

Related

• Automorphisms of the two-parameter Hopf algebra \V
• The Prime ideal Stratification and The Automorphism Group of U⁺_r,s(B₂)
• Isomorphisms between Two Quantized Enveloping Algebras of the Same Type
• (Hopf) Algebra Automorphisms of the Hopf algebra \check U^{≥ 0}_r,s(\mathfrak sl₃)
• Derivations and Hochschild cohomology of quantum nilpotent algebras