Deformations of classical Lie algebras with homogeneous root system in characteristic two. I

Spaces of local deformations of classical Lie algebras with a homogeneous root system over a field $K$ of characteristic 2 are studied. By a classical Lie algebra over a field $K$ we mean the Lie algebra of a simple algebraic Lie group or its quotient algebra by the centre. The description of deformations of Lie algebras is interesting in connection with the classification of the simple Lie algebras.