论文标题
在$ k $ -para-kählerlie代数$ k $ -symplectic lie代数代数
On $k$-para-Kähler Lie algebras a subclass of $k$-symplectic Lie algebras
论文作者
论文摘要
$ k $ -para-kählerlie代数是对para-kählerlie代数$（k = 1）$的概括，构成了$ k $ -symplectic lie代数的子类。在本文中，我们表明，可以将para-kählerlie代数作为左侧对称的双子骨的表征推广到$ k $ -para-kählerlie代数，从而引入了两个不同的结构，这些结构都不同，但两者都概括了左对称代数的概念。这还允许引入广义$ s $ matrices。 然后，我们确定dimension $（k+1）$的所有$ k $ -symplectic Lie代数和所有六个维度2-Para-kählerlie代数。
$k$-Para-Kähler Lie algebras are a generalization of para-Kähler Lie algebras $(k=1)$ and constitute a subclass of $k$-symplectic Lie algebras. In this paper, we show that the characterization of para-Kähler Lie algebras as left symmetric bialgebras can be generalized to $k$-para-Kähler Lie algebras leading to the introduction of two new structures which are different but both generalize the notion of left symmetric algebra. This permits also the introduction of generalized $S$-matrices. We determine then all the $k$-symplectic Lie algebras of dimension $(k+1)$ and all the six dimensional 2-para-Kähler Lie algebras.
