Inner derivations of simple Lie pencils of rank 1
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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).
KeywordsLie pencil Cartan subalgebra torus inner derivation sandwich algebra
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- 1.Kantor, I. L. and Persits, D. B. “On Closed Pencils of Linear Poisson brackets”, IX All-Union Geometric Conf. (Shtiintsa, Kishinev, 1988), p. 141.Google Scholar