Journal of Lie Theory

no. 3
Theory of Extensions of Multiplicative Lie Algebras
Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 637-658
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.
DOI: 10.5802/jolt.1190
Classification: 17B56, 19C09, 18G50
Keywords: Multiplicative Lie algebras, Schreier extensions, factor system, Lie cohomology 
@article{JOLT_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},
     doi = {10.5802/jolt.1190},
     zbl = {1486.17033},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1190/}
}
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%A S. K. Upadhyay
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M. S. Pandey; S. K. Upadhyay. Theory of Extensions of Multiplicative Lie Algebras. Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 637-658. doi: 10.5802/jolt.1190

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