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arXiv · 1207.5133

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

Hui-Xiang Chen
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Abstract

Let $k_q[x, x^{-1}, y]$ be the localization of the quantum plane $k_q[x, y]$ over a field $k$, where $0\neq q\in k$. 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 $U_q({\mathfrak sl}_2)$. 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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Hui-Xiang Chen. 2012-07-21. The Coalgebra Automorphism Group of Hopf Algebra $k_q[x, x^{-1}, y]$. https://arxiv.org/abs/1207.5133

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