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.

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Correspondence to Ivan Kaygorodov.

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The authors thank the referee of the paper for constructive comments. The work was supported by Nazarbayev University Faculty Development Competitive Research Grants N090118FD5341; Nazarbayev University Faculty Development Competitive Research Grants N090118FD5342; FAPESP 2019/03655-4; CNPq 404649/2018-1; RFBR 20-01-00030; AP08052405 of MES RK.

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Ismailov, N., Kaygorodov, I. & Mustafa, M. The algebraic and geometric classification of nilpotent right alternative algebras. Period Math Hung (2021). https://doi.org/10.1007/s10998-021-00386-x

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Keywords

  • Right alternative algebras
  • Nilpotent algebras
  • Algebraic classification
  • Central extension
  • Geometric classification
  • Degeneration

Mathematics Subject Classification

  • 17D15
  • 17A30
  • 14D06
  • 14L30