Lie algebra deformations of type $\bar{A_5}$ in characteristic $2$

Background. The classification of simple Lie algebras over an algebraically closed field of characteristic $p=2$ is not complete by now. Deformations of Lie algebras make it possible to obtain examples of new simple Lie algebras. The goal of the paper is to describe the structure of the space of local deformations as a module over automorphism group $Aut L$. Methods. Methods of deformation theory and a technique based on the study of the orbits of the action of the automorphism group of Lie algebra on the space of its local deformations are applied. Results. We find a description of the space of the local deformations of lie algebra as a quotient of the module in the standard 6-dimensional-module. Conclusions. The global deformation deformations of Lie algebra give a new simple $34$-dimensional Lie algebra of characteristic $2$.