Abstract:
We construct an additive basis for a relatively free alternative algebra of Lie-nilpotent degree 5, describe the associative center and core of this algebra, and find the T-generators of the full center. Also, we give some asymptotic estimate for the codimension of the T-ideal generated by a commutator of degree 5 in a free alternative algebra, and find a finite-dimensional superalgebra that generates the variety of alternative algebras with the Lie-nilpotency of the selfadjoint operator of degree 5.
Keywords:Lie-nilpotent algebra, alternative algebra, codimension of a T-ideal, additive basis for a free algebra, center of an algebra.
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