TENSOR-CLOSED OBJECTS IN THE BGG CATEGORY OF A QUANTIZED SEMISIMPLE LIE ALGEBRA

Year 2021, Volume: 29 Issue: 29, 175 - 186, 05.01.2021

Zhaoting Weı

https://doi.org/10.24330/ieja.852178

Cited By: 1

Abstract

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

Keywords

BGG category, quantized universal enveloping algebra, tensor product, formal character

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