The Coalgebra Automorphism Group of Hopf Algebra k_q[x, x^-1, y]

2012/07/21 by Hui-Xiang Chen, Chen, Hui-Xiang
Mathematics · #16W20 #2010: 16T15 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16T15 #msc:16W20

paper · pdf · doi:10.48550/arxiv.1207.5133

26 pages

arxiv created 2012/07/21 · arxiv updated 2012/07/24

Abstract

Let k_q[x, x^-1, y] be the localization of the quantum plane k_q[x, y] over a field k, where 0≠ q∈ k. Then k_q[x, x^-1, y] is a graded Hopf algebra, which can be regarded as the non-negative part of the quantum enveloping algebra U_q(\mathfrak sl₂). Under the assumption that q is not a root of unity, we investigate the coalgebra automorphism group of k_q[x, x^-1, y]. We describe the structures of the graded coalgebra automorphism group and the coalgebra automorphism group of k_q[x, x^-1, y], respectively.

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