Russian Mathematics

, Volume 61, Issue 4, pp 11–17 | Cite as

Inner derivations of simple Lie pencils of rank 1

Article

Abstract

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).

Keywords

Lie pencil Cartan subalgebra torus inner derivation sandwich algebra 

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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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