Bulletin of the
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Bull. Korean Math. Soc. 2023; 60(4): 1025-1034

Online first article July 13, 2023      Printed July 31, 2023

https://doi.org/10.4134/BKMS.b220460

Copyright © The Korean Mathematical Society.

Annihilator ideals of simple modules of restricted quantized enveloping algebra

Yu Wang

Jiangsu University of Technology

Abstract

Let $U$ be the restricted quantized enveloping algebra $\widetilde{U}_q(\mathfrak{sl}_2)$ over an algebraically closed field of characteristic zero, where $q$ is a primitive $l$-th root of unity (with $l$ being odd and greater than $1$). In this paper we show that any indecomposable submodule of $U$ under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of $U$. Moreover, we classify annihilator ideals of simple modules of $U$ by generators.

Keywords: Restricted quantized enveloping algebra, annihilator ideal, adjoint action

MSC numbers: 16D25, 20G42

Supported by: This work was supported by the National Natural Science Foundation of China (Grant No. 11871063).

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