TENSOR-CLOSED OBJECTS IN THE BGG CATEGORY OF A QUANTIZED SEMISIMPLE LIE ALGEBRA
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.
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- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI