The classification of n-dimensional anticommutative algebras with (n − 3)-dimensional annihilator

Abstract

We give the classification of all n-dimensional anticommutative complex algebras with (n − 3)-dimensional annihilator. Namely, we describe all central extensions of all 3-dimensional anticommutative complex algebras.

Keywords:

• Anticommutative algebra
• central extension
• classification problem

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17D99
• 18G60

Acknowledgements

The authors are thankful to the referee for the valuable remarks.

Appendix Table 1.

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Additional information

Funding

The work is supported by the PCI of the UCA “Teoría de Lie y Teoría de Espacios de Banach,” by the PAI with project numbers FQM298, FQM7156 and by the project of the Spanish Ministerio de Educación y Ciencia MTM2016-76327C31P, RFBR 17-01-00258.