On the existence of deformations of Lie algebras of $Z$ series

The paper continues the series of investigations devoted to description of filtered deformations of exceptional Lie algebras over algebraically closed fields of characteristic $p=3$. We construct the realization of filtered deformations of Lie algebras of $Z$ series as subalgebras of the infinite-dimensional algebra $Z(E)$. We prove that these deformations are non-isomorphic to the corresponding graded Lie algebras.