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<p>In this paper, we study three classes of subvarieties inside the variety of left-symmetric algebras. We show that these subvarieties are naturally related to some well-known varieties, such as alternative, assosymmetric, and Zinbiel algebras. For certain subvarieties of the varieties of alternative and assosymmetric algebras, we explicitly construct bases of the corresponding free algebras. We then define the commutator and anti-commutator operations on these algebras and derive a number of identities satisfied by these operations in all degrees up to 4.</p>

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Malcev classification for the variety of left-symmetric algebras

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • A. Ryskeldin,
  • B. Sartayev

摘要

In this paper, we study three classes of subvarieties inside the variety of left-symmetric algebras. We show that these subvarieties are naturally related to some well-known varieties, such as alternative, assosymmetric, and Zinbiel algebras. For certain subvarieties of the varieties of alternative and assosymmetric algebras, we explicitly construct bases of the corresponding free algebras. We then define the commutator and anti-commutator operations on these algebras and derive a number of identities satisfied by these operations in all degrees up to 4.