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

In the present context, we investigate to obtain some more results about 2-nilpotent multiplier M(2)(L) of a finite dimensional nilpotent Lie algebra L. For instance, we characterize the structure of M(2)(H) when H is a Heisenberg Lie algebra. Moreover, we give some inequalities on dimM(2)(L) to reduce a well known upper bound on 2-nilpotent multiplier as much as possible. Finally, we show that H(m) is 2-capable if and only if m=1.