Some inequalities for the dimension of the \(c\)-nilpotent multiplier of Lie algebras
Corresponding to the Baer invariant of a group with respect to the variety of nilpotent groups, the authors define the c-nilpotent multiplier for a Lie algebra, \(L\). When \(c=1\), one obtains the Schur multiplier of \(L\). The \(c\)-nilpotent multiplier is abelian, hence is characterized by it's dimension, and is independent of the free presentation of \(L\) that is used in it's definition. Bounds on this dimension are obtained. The related concept of c-cover of \(L\) is also studied. Unlike the case when \(c=1\), c-covers may not exist. Here one only needs to take an abelian Lie algebra of dimension at least 2 and \(c\) to be at least 2. However, for \(c\)-perfect algebras, \(c\)-covers are shown to exist.
scientific article; zbMATH DE number 5614721