# Spectral Sequences For Commutative Lie Algebras

## TL;DR

This paper develops spectral sequences to compute the cohomology of commutative Lie algebras in characteristic 2, providing new computational tools and comparison methods between different cohomology theories.

## Contribution

It introduces spectral sequences tailored for commutative Lie algebras in characteristic 2, including a Hochschild-Serre-type sequence and comparison sequences between various cohomologies.

## Key findings

- Constructed spectral sequences for cohomology calculations.
- Provided comparison tools between Chevalley-Eilenberg, commutative, and Leibniz cohomologies.
- Illustrated methods with explicit computations.

## Abstract

We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2. In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain comparison spectral sequences which mediate between Chevalley-Eilenberg-, commutative-and Leibniz cohomology. These methods are illustrated by a few computations.