
Journal of Lie Theory 34 (2024), No. 2, 423436 Copyright Heldermann Verlag 2024 The Schur Multiplier of Some Finite Multiplicative Lie Algebras Amit Kumar Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, Prayagraj, India amitkroor98@gmail.com, amitiiit007@gmail.com Deepak Pal Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, Prayagraj, India deepakpal5797@gmail.com Seema Kushwaha Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, Prayagraj, India seema28k@gmail.com Sumit Kumar Upadhyay Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, Prayagraj, India upadhyaysumit365@gmail.com We classify all the multiplicative Lie algebra structures on symmetric groups and alternating groups. We also determine the Schur multiplier and the Lie exterior square of some finite multiplicative Lie algebras. For a non abelian simple group K with trivial Schur multiplier, we see that the Schur multiplier of multiplicative Lie algebra K is trivial and the Lie exterior square of K is isomorphic to K with improper multiplicative Lie algebra structure. Keywords: Multiplicative Lie algebra, Schur multiplier, exterior square, commutator. MSC: 15A75, 19C09, 20F12. [ Fulltextpdf (141 KB)] for subscribers only. 