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Journal of Lie Theory 35 (2025), No. 2, 329--344 Copyright Heldermann Verlag 2025 Automorphisms of Multiplicative Lie Algebra Extensions Dev Karan Singh Department of Mathematics, Motilal Nehru National Inst. of Technology, Allahabad, Prayagraj, India dev.2020rma01@mnnit.ac.in Shiv Datt Kumar Department of Mathematics, Motilal Nehru National Inst. of Technology, Allahabad, Prayagraj, India sdt@mnnit.ac.in We discuss the inducibility problem for automorphisms of multiplicative Lie algebra extensions and show that obstruction to the inducibility of pairs of automorphisms lies in the second cohomology group of multiplicative Lie algebras. We also establish the Wells type exact sequence for multiplicative Lie algebras, which relates automorphism groups with the second cohomology group of multiplicative Lie algebras. Keywords: Automorphisms of multiplicative Lie algebras, cohomology group, exact sequences, split extensions. MSC: 17B40, 17B56, 18G50. [ Fulltext-pdf (140 KB)] for subscribers only. |