Titre : [FORTHCOMING] Cohomology and deformations of restricted Lie algebras and their morphisms in positive characteristic 

Auteurs : Quentin Ehret
, Abdenacer Makhlouf,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Forthcoming papers<br> 

Volume :  

Date : 2025/04/1 

DOI : TBA 

ISSN : 1869-6090 

Résumé : 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 $$$p\geq 2$$$. 

Éditeur : ISTE OpenScience