The algebraic and geometric classification of nilpotent right alternative algebras

Abstract

We present algebraic and geometric classifications of the $4$-dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are only $9$ non-isomorphic nontrivial nilpotent right alternative algebras. The corresponding geometric variety has dimension $13$ and it is determined by the Zariski closure of $4$ rigid algebras and one one-parametric family of algebras.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1903.08997, arXiv:2101.07375, arXiv:1812.01442

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Cited by in corpus (2)

• Non-associative algebraic structures: classification and structure
• The algebraic and geometric classification of right alternative and semi-alternative algebras