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Czechoslovak Mathematical Journal, Vol. 74, No. 1, pp. 283-299, 2024

Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras

Dev Karan Singh, Mani Shankar Pandey, Shiv Datt Kumar

Received June 6, 2023.   Published online January 19, 2024.
Abstract:  This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The paper presents an innovative adaptation of the Hirsch-Plotkin theorem specifically tailored for multiplicative Lie algebras.
Keywords:  multiplicative Lie algebra; commutator; nilpotent group; perfect group; central extensions
Classification MSC:  17A99, 19G24, 20A99, 20F19
DOI:  10.21136/CMJ.2024.0261-23
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Affiliations:   Dev Karan Singh (corresponding author), Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj 211004, U.P., India, e-mail: devkaransingh1811@gmail.com, dev.2020rma01@mnnit.ac.in; Mani Shankar Pandey, Department of Sciences, Indian Institute of Information Technology Design and Manufacturing Kurnool, Jagannathagattu Hill, Kurnool 518008, Andhra Pradesh, India, e-mail: mspandey@iiitk.ac.in, manishankarpandey4@gmail.com; Shiv Datt Kumar, Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj 211004, U.P., India, e-mail: sdt@mnnit.ac.in
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