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arXiv · 1807.11134

Faithful irreducible representations of modular Lie algebras

Donald W. Barnes
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Abstract

Let L be a finite-dimensional Lie algebra over a field of non-zero characteristic. By a theorem of Jacobson, L has a finite-dimensional faithful module which is completely reducible. We show that if the field is not algebraically closed, then L has an irreducible such module. We also give a necessary and sufficient condition for a finite-dimensional Lie algebra over an algebraically closed field of non-zero characteristic to have a faithful irreducible module.

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Donald W. Barnes. 2018-07-30. Faithful irreducible representations of modular Lie algebras. https://arxiv.org/abs/1807.11134

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