
Journal of Lie Theory 23 (2013), No. 2, 483492 Copyright Heldermann Verlag 2013 Some Notes on the Schur Multiplier of a Pair of Lie Algebras Behrouz Edalatzadeh Dept. of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran edalatzadeh@gmail.com We review some properties of the nonabelian 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 [ Fulltextpdf (262 KB)] for subscribers only. 