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.
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