Journal of Lie Theory

no. 2
On the Schur Multiplier and Covers of a Pair of Leibniz Algebras
Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 301-312
We utilize the notion of relative central extension on pairs of Leibniz algebras to study their Schur multipliers and covers. We provide some necessary conditions for detecting a certain class of covers of a pair of Leibniz algebras. In addition, we prove that every perfect pair of Leibniz algebras admits at least one cover. Moreover, we show that under certain conditions this cover is unique up to isomorphism. Finally, we prove that any two covers of a finite dimensional Leibniz algebra induce isoclinic pairs of Leibniz algebras.
DOI: 10.5802/jolt.1172
Classification: 17A32, 17B99
Keywords: Pair of Leibniz algebras, Schur multiplier, cover 
@article{JOLT_2021_31_2_a0,
     author = {G. R. Biyogmam and H. Safa},
     title = {On the {Schur} {Multiplier} and {Covers} of a {Pair} of {Leibniz} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {301--312},
     year = {2021},
     volume = {31},
     number = {2},
     doi = {10.5802/jolt.1172},
     zbl = {1489.17001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1172/}
}
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G. R. Biyogmam; H. Safa. On the Schur Multiplier and Covers of a Pair of Leibniz Algebras. Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 301-312. doi: 10.5802/jolt.1172

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