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Information Journal Paper

Title

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

Pages

  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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