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Abelian ideals in a Borel subalgebra of a complex simple Lie algebra

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Let \(\mathfrak{g}\) be a complex simple Lie algebra and \(\mathfrak{b}\) a fixed Borel subalgebra of \(\mathfrak{g}\). We describe the abelian ideals in \(\mathfrak{b}\) in a uniform way, that is, independent of the classification of complex simple Lie algebras. As an application we derive a formula for the maximal dimension of a commutative Lie subalgebra of \(\mathfrak{g}\).

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  1. Departement Mathematik, ETH Zürich, ETH Zentrum, 8092, Zürich, Switzerland

    Ruedi Suter

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Suter, R. Abelian ideals in a Borel subalgebra of a complex simple Lie algebra. Invent. math. 156, 175–221 (2004). https://doi.org/10.1007/s00222-003-0337-0

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  • DOI: https://doi.org/10.1007/s00222-003-0337-0

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