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arXiv · 2603.09655

Locally finite varieties of nonassociative algebras

Yuri Bahturin·Alexander Olshanskii
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Abstract

We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such as: nilpotence, solvability, simplicity, freeness, projectivity, and injectivity. We are also interested in the numerical estimates of the ratio of the number of algebras with various classical properties to the total number of all algebras of a fixed dimension $n$. Among these properties are having no proper nontrivial subalgebras or no nontrivial automorphisms, etc.

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Yuri Bahturin, Alexander Olshanskii. 2026-03-10. Locally finite varieties of nonassociative algebras. https://arxiv.org/abs/2603.09655

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