Journal of Lie Theory 29 (2019), No. 2, 303--310
Copyright Heldermann Verlag 2019
Annihilators of Simple Integrable Weight sl(∞)-Modules
Lucas Calixto
Department of Mathematics, Federal University of Minas Gerais, Pampulha, Belo Horizonte, Brazil
lhcalixto@ufmg.br
Let g = sl(∞). We compute the annihilators of a class of simple integrable weight g-modules with finite-dimensional weight spaces. It is a claim of I. Dimitrov, that this class exhausts all simple integrable weight g-modules with finite-dimensional weight spaces. The main feature of interest is that Dimitrov's modules contains non highest weight modules. Here we provide another construction for these modules, which allows to apply recent results of A. Petukhov and I. Penkov to compute such annihilators.
Keywords: Annihilator of modules, weight modules, direct limit Lie algebras.
MSC: 17B65, 17B10
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