Journal of Lie Theory 23 (2013), No. 2, 483--492
Copyright Heldermann Verlag 2013
Some Notes on the Schur Multiplier of a Pair of Lie Algebras
Dept. of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran
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.
Keywords: Schur multiplier of a pair of Lie algebras, nonabelian exterior product, cover, capability.
MSC: 17B30, 17B60, 17B99
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