论文标题
Z级的Hom-Lie Superalgebras
Z-graded Hom-Lie Superalgebras
论文作者
论文摘要
在本文中，我们介绍了Z级的Hom-Lie Superalgebras的概念，并表明有一个最大的（分别，最小）Z-raded Hom-Lie Superalgebra，用于给定的本地Hom-lie Superalgebra。此外，我们在Z级的hom-lie Superalgebra上引入了不变的双线性形式，并证明局部部分上的一致的超对称α-invariant形式可以独特地扩展到在整个Z-Graded Hom-hom-hom-lie Superalgebra上具有相同属性的双线性形式。此外，我们检查了Z级的Hom-Lie Superalgebra很简单的条件。
In this paper we introduce the notions of Z-graded hom-Lie superalgebras and we show that there is a maximal (resp., minimal) Z-graded hom-Lie superalgebra for a given local hom-Lie superalgebra. Morever, we introduce the invariant bilinear forms on a Z-graded hom-Lie superalgebra and we prove that a consistent supersymmetric α-invariant form on the local part can be extended uniquely to a bilinear form with the same property on the whole Z-graded hom-Lie superalgebra. Furthermore, we check the condition in which the Z-graded hom-Lie superalgebra is simple.
