p-Filiform Zinbiel algebras

Abstract 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 n -dimensional naturally graded p -filiform Zinbiel algebras under hypothesis n - p ⩾ 4 .