Cohomology in algebra, geometry, physicsand statistics

Commutative cohomology in characteristic 2

Commutative Lie algebras are commutative algebras in characteristic 2 satisfying
the Jacobi identity. This class of algebras is broader than the class of Lie
algebras (which satisfy the stronger alternating identity [x,x] = 0).
The natural cohomology in this class is a variation of the usual
 Chevalley-Eilenberg cohomology, where alternating cochains are
replaced by symmetric ones. This cohomology appears naturally in the
ongoing efforts to advance in classification of simple Lie algebras in
characteristic 2, and its properties resemble cohomology of Lie
superalgebras (in any characteristic) rather than the usual
Chevalley-Eilenberg cohomology. We will discuss some general results,
computations, and open questions. (Based on arXiv:1907.03690).