Journal of Lie Theory

no. 2
Some Notes on the Schur Multiplier of a Pair of Lie Algebras
Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 483-492
We review some properties of the non-abelian exterior product and using them provide special properties of the Schur multiplier of a pair of Lie algebras. By constructing a cover for a pair of Lie algebras, we give a necessary and sufficient condition for the capability of a pair of Lie algebras. Also, for a perfect pair of Lie algebras we construct a cover which is a universal extension. Finally, we give some bounds for the dimension of the Schur multiplier of a pair of Lie algebras.
DOI: 10.5802/jolt.734
Classification: 17B30, 17B60, 17B99
Keywords: Schur multiplier of a pair of Lie algebras, nonabelian exterior product, cover, capability 
@article{JOLT_2013_23_2_a6,
     author = {B. Edalatzadeh},
     title = {Some {Notes} on the {Schur} {Multiplier} of a {Pair} of {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {483--492},
     year = {2013},
     volume = {23},
     number = {2},
     doi = {10.5802/jolt.734},
     zbl = {1301.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.734/}
}
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B. Edalatzadeh. Some Notes on the Schur Multiplier of a Pair of Lie Algebras. Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 483-492. doi: 10.5802/jolt.734

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