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 \(\textrm{PGL}(6)\) correspond to \(\textrm{GL}(V)\)-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.

中文翻译：

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特征2中的$$ \ bar {\ boldsymbol {A}} _ {\ mathbf {5}} $$类型的李代数的整体变形

摘要

证明了关于自同构群\ {的特征2的代数封闭域\（K \）上的李代数\（\ bar {A} _ {5} \）的局部变形空间的轨道。\ textrm {PGL}（6）\）对应于\（\ textrm {GL}（V）\） -6维空间三向量的轨道。对于与秩为\（\ rho <6 \）的三向量相对应的局部变形，证明了可积性，并构造了整体变形。