Journal of Lie Theory 31 (2021), No. 3, 637--658
Copyright Heldermann Verlag 2021
Theory of Extensions of Multiplicative Lie Algebras
Mani Shankar Pandey
Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, India
manishankarpandey4@gmail.com
Sumit Kumar Upadhyay
Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, India
upadhyaysumit365@gmail.com
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.
Keywords: Multiplicative Lie algebras, Schreier extensions, factor system, Lie cohomology.
MSC: 17B56, 19C09, 18G50.
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