On linear subspaces of nilpotent elements in a Lie algebra
Let \(L\) be a complex semisimple Lie algebra. The authors show that if \(W\) is a linear subspace of ad-nilpotent elements, then \(\dim W\leq \frac 12(\dim L-\operatorname {rank }L)\). They also prove that the maximal dimension of a linear space of symmetric nilpotent \(n\times n\) complex matrices is \(\frac 14 n^2\).
scientific article; zbMATH DE number 1355349