Geodesic
Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra $U_{r,s}(\mathfrak {sl}_2)$
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 715-731.

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Let $U$ be the two-parameter quantized enveloping algebra $U_{r,s}(\mathfrak {sl}_2)$ and $F(U)$ the locally finite subalgebra of $U$ under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of $F(U)$ in the case when $rs^{-1}$ is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of $U$ by generators.
DOI : 10.21136/CMJ.2023.0193-22
Classification : 16D25, 20G42
Keywords: two-parameter quantum group; locally finite subalgebra; adjoint action; annihilator ideal 
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Wang, Yu; Li, Xiaoming. Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra $U_{r,s}(\mathfrak {sl}_2)$. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 715-731. doi : 10.21136/CMJ.2023.0193-22. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0193-22/

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