p-filiform Zinbiel algebras
L.M. CamachoDpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainE.M. CañeteDpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainS. Gómez-VidalDpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainB. A. OmirovInstitute of Mathematics and Information Technologies of Academy of Uzbekistan, 29, F. Hodjaev srt., 100125 Tashkent, Uzbekistan
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Аннотация
The paper deals with the classification of a subclass of finite-dimensional Zinbiel algebras: the naturally graded p-filiform Zinbiel algebras. A Zinbiel algebra is the dual to Leibniz algebra in Koszul sense. We prove that there exists, up to isomorphism, only one family of naturally graded p-filiform Zinbiel algebras under hypothesis $n-p \geq 4.$
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