Some inequalities for the dimension of the Schur multiplier of a pair of (nilpotent) Lie algebras (Q435933)

For a pair of Lie algebras \((L,N)\) where \(N\) is an ideal in \(L\), the authors define the Schur multiplier, \(M(L,N)\), of the pair. The corresponding concept has already been defined by \textit{G. Ellis} for groups [Appl. Categ. Struct. 6, No. 3, 355--371 (1998; Zbl 0948.20026)]. The authors determine inequalities for the dimension of \(M(L,N)\). Particular results are found when \(L\) is nilpotent. They also find a relationship between the dimension of the Schur multiplier for a pair of Lie algebras and the dimension of the Schur multiplier of a pair of factor algebras