On linear subspaces of nilpotent elements in a Lie algebra Original Research Article

Let g be a complex semi-simple Lie algebra. Extending a result of Gerstenhaber on spaces of nilpotent matrices, it is shown that if W subset of g is a linear subspace of ad nilpotent elements then dim image (dim g — rank g). Similarly, it is shown that the maximal dimension of a linear space of symmetric nilpotent n × n complex matrices is [image].