2018•Forum MathematicumRequires access

Right 2-Engel elements, central automorphisms and commuting automorphisms of Lie algebras

Mohammad Hossein Jafari, Ali Reza Madadi

Abstract

Abstract In the present paper, right 2-Engel elements, central automorphisms and commuting automorphisms of Lie algebras will be studied. For this purpose, first the structure of the set of all right 2-Engel elements of a Lie algebra will be examined and then, by taking advantage of it, a number of interesting results about central and commuting automorphisms of Lie algebras will be presented. Finally, a characterization of Lie algebras for which the set of central automorphisms is trivial or the set of commuting automorphisms is trivial will be given.

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Key concepts: Automorphism, Mathematics, Automorphisms of the symmetric and alternating groups, Pure mathematics, Lie algebra, Set (abstract data type), Lie conformal algebra, Non-associative algebra