Journal of Lie Theory 34 (2024), No. 2, 423--436
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.
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