THE ALGEBRAIC AND GEOMETRIC CLASSIFICATION OF NILPOTENT NONCOMMUTATIVE JORDAN ALGEBRAS
Dilfuza TashpulotovaTeacher of Methodology of preschool and primary education Shakhrisabz branch of Tashkent State Pedagogical University named after Nizami
ABI
Abstract
We give algebraic and geometric classifications of complex 4-dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only 18 non-isomorphic nontrivial nilpotent noncommutative Jordan algebras. The corresponding geometric variety is determined by the Zariski closure of 3 rigid algebras and 2 one-parametric families of algebras.
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