Global deformations of a Lie algebra of type $\bar{A_5}$

Abstract

It is shown that the orbits of the space of local deformations of the Lie algebra $\bar{A_5}$ over an algebraically closed field $K$ of characteristic 2 with respect to the automorphism group $\mathrm{PGL} (6)$ correspond to $\mathrm{GL} (V)$-orbits of tri-vectors of a 6-dimensional space. For local deformations corresponding to tri-vectors of rank $\rho <6$, integrability is proved and global deformations are constructed.