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Keywords:
two-parameter quantum group; locally finite subalgebra; adjoint action; annihilator ideal
two-parameter quantum group; locally finite subalgebra; adjoint action; annihilator ideal
Summary:
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.
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