论文标题
Hom-Lie代数结构上的二次谎言代数和扭曲的杀戮状形式定义了
Hom-Lie algebra structures on quadratic Lie algebras and twisted invariant Killing-like forms defined on them
论文作者
论文摘要
在给定的二次谎言代数的中央扩展中定义的hom-lie代数反过来允许不变的度量。显示了其中一些代数如何自然配备其他对称的双线性形式，这些形式满足其扭曲乘法图的不变条件。如此获得的扭曲的不变双线形式类似于普通谎言代数定义的cartan杀伤形式。这一事实允许研究对Hom-Lie代数进行研究，其中一些与普通的cartan杀伤形式相关的结果。
Hom-Lie algebras defined on central extensions of a given quadratic Lie algebra that in turn admit an invariant metric, are studied. It is shown how some of these algebras are naturally equipped with other symmetric, bilinear forms that satisfy an invariant condition for their twisted multiplication maps. The twisted invariant bilinear forms so obtained resemble the Cartan-Killing forms defined on ordinary Lie algebras. This fact allows one to reproduce on the Hom-Lie algebras hereby studied, some results that are classically associated to the ordinary Cartan-Killing form.
