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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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 84, 18–30 (2022). https://doi.org/10.1007/s10998-021-00386-x
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DOI: https://doi.org/10.1007/s10998-021-00386-x
Keywords
- Right alternative algebras
- Nilpotent algebras
- Algebraic classification
- Central extension
- Geometric classification
- Degeneration