What question did this study set out to answer?

This research aims to explore the second non-abelian cohomology of Lie algebras using crossed modules.

March 29, 2026Open Access

Non-Abelian Cohomology and Extensions of Lie Algebras

Key Points

This research aims to explore the second non-abelian cohomology of Lie algebras using crossed modules.
Introduce a generalized notion of Lie algebra of derivations.
Establish a relationship between cohomology and Lie algebra extensions.
Extend an existing seven-term exact cohomology sequence to nine terms.
Successfully establish a new connection between non-abelian cohomology and Lie algebra extensions.
Extend the existing cohomology sequence framework, enhancing its mathematical application.

Abstract

We introduce the second non-abelian cohomology of Lie algebras with coefficients in crossed modules using the generalised notion of Lie algebra of derivations, and establish a relationship of this cohomology with Lie algebra extensions by crossed modules.We extend the seven-term exact non-abelian cohomology sequence of Guin to a nine-term exact sequence.

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Cite This Study

Inassaridze et al. (Tue,) studied this question.

synapsesocial.com/papers/69c8c15ade0f0f753b39bbf5 https://doi.org/https://doi.org/10.5802/jolt.503

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