Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2406.07552
 arXiv:
 arXiv:2406.07552
 Bibcode:
 2024arXiv240607552M
 Keywords:

 Mathematics  Rings and Algebras
 EPrint:
 26 page