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The algebraic and geometric classification of nilpotent right alternative algebras

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 Added by Ivan Kaygorodov
 Publication date 2021
  fields
and research's language is English




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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.



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