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

Authors : Zhaoting WEI

Pages : 175-186

Doi:10.24330/ieja.852178

View : 102 | Download : 12

Publication Date : 2021-01-05

Article Type : Research Paper

Abstract :We consider the BGG category $\O$ of a quantized universal enveloping algebra $U_qinsert ignore into journalissuearticles values(\mathfrak{g});$. 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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