Geodesic
On the Schur Multiplier and Covers of a Pair of Leibniz Algebras
Journal of Lie theory, Tome 31 (2021) no. 2, pp. 301-312
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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.
Classification : 17A32, 17B99
Mots-clés : Pair of Leibniz algebras, Schur multiplier, cover 
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     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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2021_31_2_JLT_2021_31_2_a0/}
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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, Tome 31 (2021) no. 2, pp. 301-312. http://geodesic.mathdoc.fr/item/JLT_2021_31_2_JLT_2021_31_2_a0/