Minimal faithful representations of reductive Lie algebras

Dietrich Burde; Wolfgang Moens

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Minimal faithful representations of reductive Lie algebras

Dietrich Burde·Wolfgang Moens

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Abstract

We prove an explicit formula for the invariant $μ(\Lg)$ for finite-dimensional semisimple, and reductive Lie algebras $\Lg$ over $\C$. Here $μ(\Lg)$ is the minimal dimension of a faithful linear representation of $\Lg$. The result can be used to study Dynkin's classification of maximal reductive subalgebras of semisimple Lie algebras.

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BibTeX RIS

Dietrich Burde, Wolfgang Moens. 2007-03-22. Minimal faithful representations of reductive Lie algebras. https://arxiv.org/abs/math/0703657

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