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.
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Acknowledgment
The author is grateful to the referee for the careful reading of the article and a series of remarks contributing to its improvement.
Funding
This research was supported by the Russian Science Foundation (Grant no. 22–11–00081).
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Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 1, pp. 164–179. https://doi.org/10.33048/smzh.2024.65.113
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Pchelintsev, S.V. Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5. Sib Math J 65, 139–152 (2024). https://doi.org/10.1134/S0037446624010130
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DOI: https://doi.org/10.1134/S0037446624010130
Keywords
- Lie-nilpotent algebra
- alternative algebra
- codimension of a T-ideal
- additive basis for a free algebra
- center of an algebra