TY - JOUR
T1 - The algebraic and geometric classification of nilpotent right alternative algebras
AU - Ismailov, Nurlan
AU - Kaygorodov, Ivan
AU - Mustafa, Manat
N1 - Funding Information:
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.
Publisher Copyright:
© 2021, Akadémiai Kiadó, Budapest, Hungary.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - Algebraic classification
KW - Central extension
KW - Degeneration
KW - Geometric classification
KW - Nilpotent algebras
KW - Right alternative algebras
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U2 - 10.1007/s10998-021-00386-x
DO - 10.1007/s10998-021-00386-x
M3 - Article
AN - SCOPUS:85107870937
SN - 0031-5303
VL - 84
SP - 18
EP - 30
JO - Periodica Mathematica Hungarica
JF - Periodica Mathematica Hungarica
IS - 1
ER -