
Journal of Lie Theory 31 (2021), No. 3, 637658 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. [ Fulltextpdf (165 KB)] for subscribers only. 