ON LINEAR-SUBSPACES OF NILPOTENT ELEMENTS IN A LIE-ALGEBRA

Let g be a complex semi-simple Lie algebra. Extending a result of Gers tenhaber 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 th an or equal to 1/2 (dim g - rank g). Similarly, it is shown that the m aximal dimension of a linear space of symmetric nilpotent nxn complex matrices is [1/4n2] (C) 1998 Elsevier Science Inc. All rights reserved .