Solvable extensions of a class of nilpotent linear Lie algebras

摘要

Let n(>2) be a positive integer, n a maximal nilpotent subalgebra of the symplectic algebra sp(2n,F) over a field F of characteristic not 2, s a solvable Lie algebra whose nilradical is isomorphic to n. The derivations of n are shown to be the sum of several types standard derivations. The dimension of s is shown at most dim(n)+n, and s is isomorphic to the standard Borel subalgebra b of sp(2n,F) if and only if dim(s)=dim(n)+n.