Inner derivations of simple Lie pencils of rank 1

Abstract

© 2017, Allerton Press, Inc.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 M3(U,D′), where U is the subspace of all skew-symmetric matrices in M3(P) and D′ is any subspace containing 〈E〉 in the space of all diagonal matrices D in M3(P).