Geodesic
Theory of Extensions of Multiplicative Lie Algebras
Journal of Lie theory, Tome 31 (2021) no. 3, pp. 637-658
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We define the second cohomology of a multiplicative Lie algebra K with coefficients in an abelian group H with trivial multiplicative Lie algebra structure in two different cases. Consequently, we prove a natural bijective correspondence between the second cohomology and the set of equivalence classes of some special type of extensions. We also define the notion of Baer sum of extensions for multiplicative Lie algebras.
Classification : 17B56, 19C09, 18G50
Mots-clés : Multiplicative Lie algebras, Schreier extensions, factor system, Lie cohomology 
@article{JLT_2021_31_3_JLT_2021_31_3_a2,
     author = {M. S. Pandey and S. K. Upadhyay},
     title = {Theory of {Extensions} of {Multiplicative} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {637--658},
     year = {2021},
     volume = {31},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a2/}
}
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M. S. Pandey; S. K. Upadhyay. Theory of Extensions of Multiplicative Lie Algebras. Journal of Lie theory, Tome 31 (2021) no. 3, pp. 637-658. http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a2/