On some property of an irreducible subalgebra of the general linear Lie algebra gl(n,R)

Summary A subalgebrag ofgl(n, R) which admits no proper invariant subspace in Rⁿ and contains a subalgebra of a special kind is studied. It is concluded that only four cases are possible if n is even, and only two if n is odd. To Enrico Bompiani on his scientific Jubilee