Some notes on the Schur multiplier of a pair of Lie algebras (Q2844754)

The author defines capability of a pair of Lie algebras \((L,N)\) in terms of admitting a crossed module and finds a condition that characterizes capability. Then crossed modules are used to define a cover of the pair and covers are shown to exist in the finite dimensional case. A pair \((L,N)\) is called perfect if \([L,N]=N\). Covers of perfect pairs are constructed. Then bounds are found on the dimension of the Schur multiplier of pairs.