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

Abstract

In the present context, we investigate to obtain some more results about $2$-nilpotent multiplier ${\mathcal{M}}^{(2)}(L)$ of a finite dimensional nilpotent Lie algebra $L$. For instance, we characterize the structure of ${\mathcal{M}}^{(2)}(H)$ when $H$ is a Heisenberg Lie algebra. Moreover, we give some inequalities on $\dim {\mathcal{M}}^{(2)}(L)$ 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.

Cited by in corpus (2)

• On $2$-Nilpotent Multiplier of Lie Superalgebras
• Characterizing nilpotent Lie algebras rely on the dimension of their $2$-nilpotent multipliers