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<p>In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of complex 3-dimensional noncommutative Jordan algebras. As a byproduct, we obtain the classification of complex 3-dimensional Kokoris, standard, generic Poisson, and generic Poisson–Jordan algebras; and also complex 4-dimensional nilpotent Kokoris and standard algebras. In addition, we consider the geometric classification of varieties of cited algebras, that is the description of its irreducible components.</p>

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The Algebraic and Geometric Classification of Noncommutative Jordan Algebras

  • 期刊论文

  • 发表日期：

    2025年11月15日

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  • Hani Abdelwahab,
  • Kobiljon Abdurasulov,
  • Ivan Kaygorodov

摘要

In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of complex 3-dimensional noncommutative Jordan algebras. As a byproduct, we obtain the classification of complex 3-dimensional Kokoris, standard, generic Poisson, and generic Poisson–Jordan algebras; and also complex 4-dimensional nilpotent Kokoris and standard algebras. In addition, we consider the geometric classification of varieties of cited algebras, that is the description of its irreducible components.