WITHDRAWN: OnLie-isoclinic Leibniz algebras

A study of n-Lie-isoclinic Leibniz algebras

“…Remark 3.3 Clearly, 0-Lie-isoclinism coincides with isomorphism and 1-Lie-isoclinism coincides with the notion of Lie-isoclinism given in [3]. Proposition 3.4 n-Lie-isoclinism is an equivalence relation.…”

“…Recently, the concept of isoclinism of Lie algebras has been considered in the relative context, given rise to the notion of Lie-isoclinism of Leibniz algebras [3]. Relative means that the notion of Lie-isoclinism arises through the Liezation functor (−) Lie : Leib → Lie which assigns the Lie algebra g Lie = g/ < {[x, x] :…”

“…This philosophy comes from the categorical theory of central extensions relative to a chosen Birkhoff subcategory of a semiabelian category. We refer to [3,7,8] and references given therein for a detailed explanation.…”

The c-nilpotent Schur Lie-multiplier of Leibniz algebras

“…Since Leib is a category of interest (see [10]), hence is a category of Ω-groups, and following Proposition 4.3.2 in [19] we can conclude that the collection of all nilpotent objects of class ≤ c in Leib form a variety. Now following [15,Proposition 7.8], it can be showed that M Lie (q) is the Schur Lie-multiplier of a Leibniz algebra q (see [9,12]). [12]).…”

“…In the recent papers [9,11,12] authors approached the relative theory of Leibniz algebras with respect to the Liezation functor, yielding to the introduction of new notions of central extensions, capability, nilpotency, stem cover, isoclinism and Schur multiplier relative to the Liezation functor, the so-called Lie-central extensions, Lie-capability, Lie-nilpotency, Lie-stem cover, Lie-isoclinism and Schur Lie-multiplier.…”