Classification of Naturally Graded Zinbiel Algebras with Characteristic Sequence Equal to (n–p, p)

Abstract

This work is a continuation of the description of some classes of nilpotent Zinbiel algebras. We focus on the study of Zinbiel algebras with restrictions to gradation and characteristic sequence. Namely, the classification of naturally graded Zinbiel algebras with characteristic sequence equal to (n − p, p) is obtained.2010 Mathematics Subject Classification. 17A30, 17A32.

Unified products for Zinbiel 2-algebras

“…It is also known as Tortkara algebras, pre-commutative and chronological algebras [24,27]. The classification of low dimensional Zinbiel algebras was investigated in [1, 2,16,25,26,32]. According to operad theory, Zinbiel algebras are Koszul dual to Leibniz algebras.…”

Central extensions of filiform Zinbiel algebras

“…Zinbiel algebras were introduced by Loday in [43] and studied in [2,5,10,17,[20][21][22]41,[44][45][46]49]. Under the Koszul duality, the operad of Zinbiel algebras is dual to the operad of Leibniz algebras.…”