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

TL;DR

This paper studies the local and global deformations of a specific Lie algebra of type A_5 over a field of characteristic 2, linking deformation orbits to tri-vectors and constructing deformations for certain ranks.

Contribution

It establishes a correspondence between deformation orbits and tri-vectors, proves integrability for low-rank cases, and constructs explicit global deformations.

Findings

Deformation orbits correspond to - orbits of tri-vectors.

Integrability is proved for tri-vectors of rank less than 6.

Explicit global deformations are constructed for low-rank cases.

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.