量子群Uq(sl3)的多项式模

Pub Date : 2022-12-01 DOI:10.1142/s1005386722000475

L. Xia, Qianqian Cai, Jiao Zhang

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引用次数: 0

摘要

设[公式:见文]为具有Cartan子代数的有限维复单李代数[公式:见文]。那么，当且仅当[Formula: see text]的类型为[Formula: see text]或[Formula: see text]时，[Formula: see text]具有[Formula: see text]-模块结构;这叫做第1阶的多项式模。在量子版本中，[公式:见文本]上的1阶多项式模块已被分类。本文证明了量子群[公式:见文]不存在秩一多项式模。

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The Polynomial Modules over Quantum Group Uq(sl3)

Let [Formula: see text] be a finite dimensional complex simple Lie algebra with Cartan subalgebra [Formula: see text]. Then [Formula: see text] has a [Formula: see text]-module structure if and only if [Formula: see text] is of type [Formula: see text] or of type [Formula: see text]; this is called the polynomial module of rank one. In the quantum version, the rank one polynomial modules over [Formula: see text] have been classified. In this paper, we prove that the quantum group [Formula: see text] has no rank one polynomial module.

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