Isomorphisms and automorphisms of quantum groups

2009/10/09 by Li, Li-Bin, Yu, Jie-Tai
#16G10 #16S10 #16W20 #16Z05 #17B10 #20C30 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0910.1713

Abstract

We consider isomorphisms and automorphisms of quantum groups. Let k be a field and suppose p, q∈ k^* are not roots of unity. We prove that the two quantum groups U_q(\mathfrak sl₂) and U_p(\mathfraksl₂) over a field k are isomorphic as k-algebras if and only if p=q^{± 1}. We also rediscover the description of the group of all k-automorphisms of U_q(\mathfraksl₂) of Alev and Chamarie, and that Aut_k(U_q(\mathfrak sl₂)) is isomorphic to Aut_k(U_p(\mathfrak sl₂)).

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