Abstract
A Lie algebra morphism triple is a triple \((\mathfrak {g}, \mathfrak {h}, \phi )\) consisting of two Lie algebras \(\mathfrak {g}, \mathfrak {h}\) and a Lie algebra homomorphism \(\phi : \mathfrak {g} \rightarrow \mathfrak {h}\). We define representations and cohomology of Lie algebra morphism triples. As applications of our cohomology, we study some aspects of deformations, abelian extensions of Lie algebra morphism triples and classify skeletal sh Lie algebra morphism triples. Finally, we consider the cohomology of Lie group morphism triples and find a relation with the cohomology of Lie algebra morphism triples.
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The author would like to thank IIT Kanpur, India where some parts of the work have been carried out.
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Communicated by Yuri Berest.
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Das, A. Cohomology of Lie Algebra Morphism Triples and Some Applications. Math Phys Anal Geom 26, 26 (2023). https://doi.org/10.1007/s11040-023-09468-3
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DOI: https://doi.org/10.1007/s11040-023-09468-3
Keywords
- Lie algebra morphism triples
- Cohomology
- Deformations
- Sh Lie algebra morphism triples
- Lie group morphism triples