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arXiv · 1001.0154

Isomorphisms between quantum groups $U_q(\mathfrak{sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$

Li-Bin Li·Jie-Tai Yu
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Abstract

Let $\mathbb K$ be a field and suppose $p, q\in\mathbb K^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$ are isomorphic as $\mathbb K$-algebras implies that $p=\pm q^{\pm 1}$ when $n$ is even. This new result answers a classical question of Jimbo.

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Li-Bin Li, Jie-Tai Yu. 2012-02-22. Isomorphisms between quantum groups $U_q(\mathfrak{sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$. https://arxiv.org/abs/1001.0154

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