Let consider $L$ be a Leibniz algebra which is left nilpotent. ( I do not know what is left nilpotent of class 3).
A Leibniz algebra L is said to be nilpotent, if for lower central series there exists n ∈ N such that $L^{n} = 0$. The minimal number $n$ with this property is said to be index of nilpotency of algebra $L$. Is the class of nilpotency the same with index of nilpotency?
An n-dimensional Leibniz algebra is called null filiform if $dim L^{i}=n+1-i$, where $1 \leq i \leq n+1$. Is a left nilpotent Leibniz algebra of class 3 a null filiform Leibniz algebras?
An algebra $A$ is called left Leibniz, if its multiplication satisfies the left Leibniz identity $$ (ab) c = a (bc) − b (ac) $$ for all $a, b, c ∈ A$. The $2$-sided ideals $A^i$ and $A_i$ are defined by $A^1=A$ and $A^{i+1}=AA^i$, and $A_1=A$, $A_{i+1}=\sum_{p=1}^iA_pA_{i+1-p}$, from the left. Then $A$ is called left nilpotent if $A_n=0$ for some $n$. One can show that $A_n=A^n$ for all $n\ge 1$.