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<p>The degenerations of Poisson-type algebras are studied in the following varieties in dimension two: Leibniz–Poisson algebras, transposed Leibniz–Poisson algebras, Novikov–Poisson algebras, commutative pre-Lie algebras, anti-pre-Lie Poisson algebras and pre-Poisson algebras. For these varieties, the algebraic and geometric classifications are given. Also, the complete graph of degenerations is obtained, together with the description of the orbit closures of each of its algebras and parametric families up to isomorphism.</p>

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Degenerations of Poisson-type algebras

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Hani Abdelwahab,
  • Amir Fernández Ouaridi,
  • Ivan Kaygorodov

摘要

The degenerations of Poisson-type algebras are studied in the following varieties in dimension two: Leibniz–Poisson algebras, transposed Leibniz–Poisson algebras, Novikov–Poisson algebras, commutative pre-Lie algebras, anti-pre-Lie Poisson algebras and pre-Poisson algebras. For these varieties, the algebraic and geometric classifications are given. Also, the complete graph of degenerations is obtained, together with the description of the orbit closures of each of its algebras and parametric families up to isomorphism.