PlanetMath: rank (Lie algebra)

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rank (Lie algebra)

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Let $\mathfrak{g}$ be a finite dimensional Lie algebra. One can show that all Cartan subalgebras $\mathfrak{h}\subset\mathfrak{g}$ have the same dimension. The rank of $\mathfrak{g}$ is defined to be this dimension.

"rank (Lie algebra)" is owned by rmilson. [ full author list (2) ]

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Cross-references: dimension, Cartan subalgebras, Lie algebra, finite dimensional
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This is version 9 of rank (Lie algebra), born on 2002-02-21, modified 2006-09-23.
Object id is 2348, canonical name is Rank.
Accessed 4495 times total.

Classification:

17B20 (Nonassociative rings and algebras :: Lie algebras and Lie superalgebras :: Simple, semisimple, reductive )

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