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Central extensions of filiform Zinbiel algebras

L.M. CamachoUniversity of Sevilla, Sevilla, SpainI. A. KarimjanovAndijan State University, Andijan, UzbekistanIvan KaygorodovCMCC, Universidade Federal do ABC, Santo André, BrazilAbror KhudoyberdiyevInstitute of Mathematics Academy of Sciences of Uzbekistan, National University of Uzbekistan, Tashkent, Uzbekistan
idUS (Universidad de Sevilla)repository2021en
ABI

Abstract

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

Topics

Advanced Topics in AlgebraAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic Topology

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