Non-singular derivations of solvable Lie algebras in prime characteristic

2018/10/29 by Lima, Marcos Goulart, Schneider, Csaba
#15A21 #17B05 #17B30 #17B40 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1810.12386

Abstract

We study solvable Lie algebras in prime characteristic p that admit non-singular derivations. We show that Jacobson's Theorem remains true if the quotients of the derived series have dimension less than~p. We also study the structure of Lie algebras with non-singular derivations in which the derived subalgebra is abelian and has codimension~one. The paper presents some new examples of solvable, but not nilpotent, Lie algebras of derived length~3 with non-singular derivations.

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