Journal of Lie Theory

no. 2
The Schur Multiplier of Some Finite Multiplicative Lie Algebras
Amit Kumar1; Deepak Pal1; Seema Kushwaha1; Sumit Kumar Upadhyay1
1Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, Prayagraj, India
Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 423-436
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.
DOI: 10.5802/jolt.1341
Classification: 15A75, 19C09, 20F12
Keywords: Multiplicative Lie algebra, Schur multiplier, exterior square, commutator

Amit Kumar  1 ; Deepak Pal  1 ; Seema Kushwaha  1 ; Sumit Kumar Upadhyay  1

1 Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, Prayagraj, India 
Amit Kumar; Deepak Pal; Seema Kushwaha; Sumit Kumar Upadhyay. The Schur Multiplier of Some Finite Multiplicative Lie Algebras. Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 423-436. doi: 10.5802/jolt.1341
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     title = {The {Schur} {Multiplier} of {Some} {Finite} {Multiplicative} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {423--436},
     year = {2024},
     volume = {34},
     number = {2},
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