The algebraic classification of nilpotent ℭ𝔇-algebras

ABSTRACT

We give an algebraic classification of complex 4-dimensional nilpotent $\mathfrak{C}\mathfrak{D}$-algebras.

Keywords:

• Nilpotent algebra
• Lie algebra
• Jordan algebra
• $\mathfrak{C}\mathfrak{D}$-algebra
• algebraic classification
• central extension

2010 Mathematics Subject Classifications:

• 17A30
• 17D99
• 17B30

Acknowledgments

The authors thank Prof. Dr Pasha Zusmanovich for discussions about $\mathfrak{C}\mathfrak{D}$-algebras.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 18/00726-5, 18/15712-0; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 404649/2018-1, 302980/2019-9; RFBR 20-01-00030.