Some Properties of the Schur Multiplier and Covers of Lie Algebras

Some inequalities for the dimension of the c-nilpotent multiplier of Lie algebras

“…This is analogous to the definition of the Baer-invariant of a group with respect to the variety of nilpotent groups of class at most c given by Baer [1] (see [4,8,9,11,12] for more information on the Baer invariant of groups). The Lie algebra M (1) (L) = M(L) is the most studied Schur multiplier of L (see for instance [2,3,14,15]). It is readily verified that the Lie algebra M (c) (L) is abelian and independent of the choice of the free presentation of L. The purpose of this paper is to obtain some inequalities for the dimension of the c-nilpotent multiplier of finite-dimensional Lie algebras and their factor Lie algebras.…”

2-capability and 2-nilpotent multiplier of finite dimensional nilpotent Lie algebras

“…It means which of them is isomorphic to H/Z 2 (H) for a Lie algebra H. For more information about the capability of Lie algebras see [18,21]. These generalized the recently results for the group theory case in [19].…”

Capability of Crossed Modules of Lie Algebras

“…In [13], it was shown, if the exact sequence of Lie algebras 0 → A → L * → L → 0 is a cover of L, that is A H 2 L and A ⊆ Z L * ∩ L * 2 , then the capability of L is equivalent to Z L * = 0. The authors represent the ideal Z L * by Z * L .…”

“…Some basic properties of covers and related concepts were discussed and extended in [1,13]. There are several tries to characterize nilpotent Lie algebras of small dimensions by their covers.…”