Some properties on Schur multiplier and cover of a pair of Lie algebras

Details Some properties on Schur multiplier and cover of a pair of Lie algebras Some properties on Schur multiplier and cover of a pair of Lie algebras

2011-04-30

arxiv.org/abs/1105.0077v1

Mathematics

Rings and Algebras

Scientific paper

Similar to works of G. Ellis (1998), the concept of covering pair of Lie algebras is defined. Also, we show the existence of covering pair for the pair of Lie algebras (L,N) and then show that every crossed module is a homomorphic image of a covering pair of (L,N). Finally, under some condition, we present some inequalities for the Schur multiplier of a pair of finite dimensional Lie algebras.

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