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March 29, 2026Journal of Lie theory0 citationsOpen Access

Non-Abelian Cohomology and Extensions of Lie Algebras

NIN. InassaridzeEKE. KhmaladzeMLM. Ladra

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. (2008) studied this question.

synapsesocial.com/papers/69c8c15ade0f0f753b39bbf5https://doi.org/10.5802/jolt.503
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