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

Abstract

Let $\mathbb{K}$ be a field and suppose $p,q\in {\mathbb{K}}^{\ast }$ 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.

This paper has been withdrawn

References in corpus (2)

• On the automorphism groups of q-enveloping algebras of nilpotent Lie algebras
• Isomorphisms and automorphisms of quantum groups

Cited by in corpus (1)

• Isomorphisms between affine Hecke algebras