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ANNIHILATOR IDEALS OF SIMPLE MODULES OF RESTRICTED QUANTIZED ENVELOPING ALGEBRA

Yu Wang
대한수학회 (The Korean Mathematical Society)|2023.07|대한수학회보 (Bulletin of the KMS)|제60권 제4호|pp. 1025-1034|DOI 10.4134/BKMS.b220460

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키워드

Restricted quantized enveloping algebraannihilator idealadjoint action
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초록

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.

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.

참고문헌 (19)

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