Central extensions of 3-dimensional Zinbiel algebras

Central extensions of 3-dimensional Zinbiel algebras

We describe all central extensions of all 3-dimensional nontrivial complex Zinbiel algebras. As a corollary, we have a full classification of 4-dimensional nontrivial complex Zinbiel algebras and a full classification of 5-dimensional nontrivial complex Zinbiel algebras with 2-dimensional annihilato...

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Veröffentlicht in:Ricerche di matematica 2023-11, Vol.72 (2), p.921-947
Hauptverfasser: Kaygorodov, Ivan, Alvarez, María Alejandra, Mello, Thiago Castilho de
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Classification
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
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Zusammenfassung:We describe all central extensions of all 3-dimensional nontrivial complex Zinbiel algebras. As a corollary, we have a full classification of 4-dimensional nontrivial complex Zinbiel algebras and a full classification of 5-dimensional nontrivial complex Zinbiel algebras with 2-dimensional annihilator, which gives the principal step in the algebraic classification of 5-dimensional Zinbiel algebras.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-021-00604-1