On linear subspaces of nilpotent elements in a Lie algebra

摘要

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 ed nilpotent elements then dim W less than or equal to 1/2 (dim g - rank g). Similarly, it is shown that the maximal dimension of a linear space of symmetric nilpotent nxn complex matrices is [1/4n2] (C) 1998 Elsevier Science Inc. All rights reserved. [References: 4]