%0 Journal Article
%T Left-symmetric algebras of derivations of free algebras
%A Ualbai Umirbaev
%J Mathematics
%D 2014
%I arXiv
%X A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric algebras of derivations are studied. Simple left-symmetric algebras of derivations and Novikov algebras of derivations are described. It is also proved that the positive part of the left-symmetric algebra of derivations of a free nonassociative symmetric $m$-ary algebra in one free variable is generated by one derivation and some right nilpotent derivations are described.
%U http://arxiv.org/abs/1412.2360v2