@ARTICLE{À venir, 

TITLE={[FORTHCOMING] Cohomologie et déformations des algèbres de Lie restreintes et leurs morphismes en caractéristique positive}, 
  
AUTHOR={Quentin Ehret
, Abdenacer Makhlouf, }, 
	
JOURNAL={Avancées en Mathématiques Pures et Appliquées}, 
	
VOLUME={}, 

NUMBER={Articles à paraître<br>}, 
	
YEAR={2025}, 

URL={https://www.openscience.fr/Cohomologie-et-deformations-des-algebres-de-Lie-restreintes-et-leurs-morphismes-en-caracteristique-positive}, 
	
DOI={À venir}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={The main purpose of this paper is  to study cohomology and develop a deformation theory of  restricted Lie algebras in positive characteristic $$$p$$$ > $$$0$$$.  In the case $$$p\geq3$$$,  it is shown that the deformations of restricted Lie algebras are controlled by the restricted cohomology introduced by Evans and Fuchs. Moreover, we introduce a new cohomology that controls the deformations of restricted morphisms of restricted Lie algebras. In the case $$$p=2$$$, we provide a full restricted cohomology complex with values in a restricted module and investigate its connections with formal deformations. Furthermore, we introduce a full deformation cohomology that controls deformations of restricted morphisms of  restricted Lie algebras in characteristic $$$2$$$. As example, we discuss restricted cohomology with adjoint coefficients of restricted Heisenberg Lie algebras in characteristic $$$p\geq 2$$$.}}