Central extensions of filiform Zinbiel algebras
L.M. CamachoUniversity of SevillaIqboljon KarimjanovAndijan State UniversityIvan KaygorodovCMCC, Universidade Federal do ABCAbror KhudoyberdiyevInstitute of Mathematics Academy of Sciences of Uzbekistan, National University of Uzbekistan
ABI
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.
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