Left-symmetric algebras of derivations of free algebras |
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| Authors: | Ualbai Umirbaev |
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| Institution: | 1. Department of Mathematics, Eurasian National University, Astana, Kazakhstan;2. Department of Mathematics, Wayne State University, Detroit, Michigan, USAumirbaev@math.wayne.edu |
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| Abstract: | 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. |
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| Keywords: | Derivations free algebras Jacobian matrices left-symmetric algebras |
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