# Commutative Lie algebras and commutative cohomology in characteristic $2$

## TL;DR

This paper explores a modified version of Chevalley--Eilenberg cohomology for Lie algebras in characteristic 2, replacing alternating cochains with symmetric ones to adapt to the field's properties.

## Contribution

It introduces a new cohomology framework for Lie algebras in characteristic 2 using symmetric cochains, differing from traditional alternating cohomology.

## Key findings

- Developed a symmetric cohomology theory for characteristic 2
- Analyzed properties of commutative Lie algebras in this setting
- Provided foundational results for future algebraic research

## Abstract

We discuss a version of the Chevalley--Eilenberg cohomology in characteristic $2$, where the alternating cochains are replaced by symmetric ones.