We describe all central extensions of $3$-dimensional non-zero complex Zinbiel algebras. As a corollary, we have full classification $4$-dimensional non-trivial algebras and $5$-dimensional with $2$-dimensional annihilator, which gives the principal step in algebraic

A well known theorem of Duflo claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is generated by its intersection with the centre. For a Lie superalgebra this result fails to be true. For instance, in the case of the orthosymplectic Lie superalgebra osp(1, 2), Pinczon gave in [Pi] an example of a Verma module whose annihilator is not gene...