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# On nilpotency of outer pointwise inner actor of the lie algebra crossed modules

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19-40

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 $i+j-1$.

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APA: Copy

Allahyari, asghar, & Saeedi, Farshid. (2020). On nilpotency of outer pointwise inner actor of the lie algebra crossed modules. JOURNAL OF MATHEMATICAL EXTENSION, 14(1), 19-40. SID. https://sid.ir/paper/743578/en

Vancouver: Copy

Allahyari asghar, Saeedi Farshid. On nilpotency of outer pointwise inner actor of the lie algebra crossed modules. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2020;14(1):19-40. Available from: https://sid.ir/paper/743578/en

IEEE: Copy

asghar Allahyari, and Farshid Saeedi, “On nilpotency of outer pointwise inner actor of the lie algebra crossed modules,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 14, no. 1, pp. 19–40, 2020, [Online]. Available: https://sid.ir/paper/743578/en

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