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arXiv · 1910.02326

Tensor-closed objects in the BGG category of a quantized semisimple Lie algebra

Zhaoting Wei
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Abstract

We consider the BGG category $\mathcal{O}$ of a quantized universal enveloping algebra $U_q(\mathfrak{g})$. We call a module $M\in \mathcal{O}$ tensor-closed if $M\otimes N\in\mathcal{O}$ for any $N\in \mathcal{O}$. In this paper we prove that $M\in \mathcal{O}$ is tensor-closed if and only if $M$ is finite dimensional. The method used in this paper applies to the unquantized case as well.

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Zhaoting Wei. 2019-10-05. Tensor-closed objects in the BGG category of a quantized semisimple Lie algebra. https://doi.org/10.24330/ieja.852178

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