The algebraic and geometric classification of nilpotent right alternative algebras
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Publication:6372582
DOI10.1007/S10998-021-00386-XzbMath1524.17014arXiv2107.05440MaRDI QIDQ6372582
I. B. Kaĭgorodov, Manat Mustafa, Nurlan Ismailov
Publication date: 2 July 2021
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.
Group actions on varieties or schemes (quotients) (14L30) Fibrations, degenerations in algebraic geometry (14D06) Nonassociative algebras satisfying other identities (17A30) Right alternative rings (17D15)
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