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

2024/02/12 by Mao, Dan, Chen, Liangyun
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2406.07552

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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• Cohomology and deformations of restricted Lie algebras and their morphisms in positive characteristic
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