Central extensions of filiform Zinbiel algebras

ABSTRACT

In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of an n-dimensional null-filiform Zinbiel algebra is isomorphic to an $(n+1)$-dimensional null-filiform Zinbiel algebra. Moreover, we obtain all pairwise non isomorphic quasi-filiform Zinbiel algebras.

KEYWORDS:

• Zinbiel algebra
• filiform algebra
• algebraic classification
• central extension

MSC2010:

• 17D25
• 17A30

Disclosure statement

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

Additional information

Funding

This work was supported by Agencia Estatal de Investigación (Spain), grant MTM2016-79661-P (European FEDER support included, UE); Russian Foundation for Basic Research (RFBR) 20-01-00030; Fundação de Amparo á Pesquisa do Estado de São Paulo - FAPESP 18/15712-0, 18/12197-7, 19/00192-3.