Leibniz Algebras, whose all subalgebras are ideals
DOI:
https://doi.org/10.15407/dopovidi2017.06.009Keywords:
Abelian subalgebras, bilinear form, center of a Leibniz algebra, cyclic subalgebra, extraspecial subalgebra, Leibniz algebra, Lie algebra, nilpotent subalgebrasAbstract
An algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra), if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] — [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras. A description of Leibniz algebras, whose subalgebras are ideals, is given.
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