@article{Saeedi_Akbarossadat_2021, title={On the Dimension of Non-Abelian Tensor Squares of $n$-Lie Algebras}, volume={52}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3373}, DOI={10.5556/j.tkjm.52.2021.3373}, abstractNote={<p>Let $L$ be an $n$-Lie algebra over a field $\mathbb{F}$. In this paper, we introduce the notion of non-abelian tensor square $L\otimes L$ of $L$ and define the central ideal $L\square L$ of it. Using techniques from group theory and Lie algebras, we show that that $L\square L\cong L^{ab}\square L^{ab}$. Also, we establish the short exact sequence<br />\[ 0\to\mathcal{M}(L)\to\frac{L\otimes L}{L\square L}\to L^2\to 0 \]<br />and apply it to compute an upper bound for the dimension of non-abelian tensor square of $L$.</p>}, number={3}, journal={Tamkang Journal of Mathematics}, author={Saeedi, Farshid and Akbarossadat, Nafiseh}, year={2021}, month={Aug.}, pages={363–381} }