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arXiv · 2406.07552

Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2

Dan Mao·Liangyun Chen
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Abstract

This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLieDer pair and the corresponding cohomology complex. We show that a ResLieDer pair is rigid if the second cohomology group is trivial and a deformation of order $n$ is extensible if and only if its obstruction class is trivial. Moreover, we prove that the central extensions of a ResLieDer pair are classified by the second cohomology group. Finally, we show that a pair of restricted derivations is extensible if and only if its obstruction class is trivial.

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Dan Mao, Liangyun Chen. 2024-02-12. Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2. https://arxiv.org/abs/2406.07552

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