Inner derivations of simple Lie pencils of rank 1

We prove that simple Lie pencils of rank 1 over an algebraically closed field P of characteristic 0 with operators of left multiplication being derivations are of the form of a sandwich algebra M 3 ( U , D ′), where U is the subspace of all skew-symmetric matrices in M 3 ( P ) and D ′ is any subspace containing 〈 E 〉 in the space of all diagonal matrices D in M 3 ( P ).