# rank (Lie algebra)

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.

Title rank (Lie algebra) RankLieAlgebra 2013-03-22 12:25:07 2013-03-22 12:25:07 rmilson (146) rmilson (146) 12 rmilson (146) Definition msc 17B20 rank