On Nilpotency of Outer Pointwise Inner Actor of the Lie Algebra Crossed Modules

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let $\mathcal{L}$ be a Lie algebra crossed module and $\Act_{pi}(\mathcal{L})$ be a point wise inner Actor of $\mathcal{L}$. In this paper, we introduce lower and upper central series of $\mathcal{L}$ and show that if $\Act_{pi}(\frac{\mathcal{L}}{Z_j(\mathcal{L})}) / \Inn\Act(\frac{\mathcal{L}}{Z_j(\mathcal{L})}) $ is the nilpotent of class $k$, then $\Act_{pi}(\mathcal{L}) / \Inn\Act(\mathcal{L}) $ is the nilpotent of the maximum class $ j+k $. Moreover, if $ \dim(\mathcal{L}^i / (\mathcal{L}^i\cap Z_j(\mathcal{L})))\leqslant 1 $, then $ \Act_{pi}(\mathcal{L}) / \Inn\Act(\mathcal{L})$ is the nilpotent of the maximum class $ i+j-1$.

Language:
English
Published:
Journal of Mathematical Extension, Volume:14 Issue: 1, Winter 2020
Pages:
19 to 40
https://www.magiran.com/p2262753