TY  - Type of reference 
TI  - [FORTHCOMING] Cohomology and deformations of restricted Lie algebras and their morphisms in positive characteristic 
AU  - Quentin Ehret
 
AU  - Abdenacer Makhlouf 
AB  - 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 $$$p\geq 2$$$. 
DO  - TBA 
JF  - Advances in Pure and Applied Mathematics 
KW  - Modular Lie algebra, restricted cohomology, deformation, Modular Lie algebra, restricted cohomology, deformation,  
L1  -  
LA  - en 
PB  - ISTE OpenScience 
DA  - 2025/04/1 
SN  - 1869-6090 
TT  - [FORTHCOMING] Cohomologie et déformations des algèbres de Lie restreintes et leurs morphismes en caractéristique positive 
UR  - https://www.openscience.fr/Cohomology-and-deformations-of-restricted-Lie-algebras-and-their-morphisms-in 
IS  - Forthcoming papers<br> 
VL  -  
ER  -