论文标题
在二次Hom-hom-lie代数上，其质心中有扭曲地图及其与二次谎言代数的关系
On quadratic Hom-Lie algebras with twist maps in their centroids and their relationship with quadratic Lie algebras
论文作者
论文摘要
研究了质心中具有不可变形的扭曲图的Hom-Lie代数。获得具有这些特性的HOM-LIE代数的中央延伸，并显示了如何保留相同特性的。给出条件，使得所产生的中央扩展对其hom-lie产品具有不变的度量，这使得在原始的hom-lie代数具有这样的度量时，其扭曲地图自动化。这项工作的重点是具有这些属性的代数，并在Benayadi和Makhloufwe之后称它们为二次Hom-Lie代数。据展示了二次霍姆·洛伊代数如何产生二次谎言代数，并且与给定的hom-lie中央扩展相关的谎言代数是其的lie代数延伸。还表明，如果Hom-Lie产品不是谎言产品，则存在非亚伯式代数，该代数也是一般的非缔合性，其产品的换向器正是Hom-Lie Central扩展的霍姆·莱（Hom-Lie）产品。此外，如果相关的谎言代数为nilpotent，则换向者意识到这种hom-lie产品的代数被证明很简单。提供了非平凡的例子。
Hom-Lie algebras having non-invertible twist maps in their centroids are studied. Central extensions of Hom-Lie algebras having these properties are obtained and shown how the same properties are preserved. Conditions are given so that the produced central extension has an invariant metric with respect to its Hom-Lie product making its twist map self-adjoint when the original Hom-Lie algebra has such a metric. This work is focused on algebras with these properties and following Benayadi and Makhloufwe call them quadratic Hom-Lie algebras. It is shown how a quadratic Hom-Lie algebra gives rise to a quadratic Lie algebra and that the Lie algebra associated to the given Hom-Lie central extension is a Lie algebra central extension of it. It is also shown that if the Hom-Lie product is not a Lie product, there exists a non-abelian algebra, which is in general non-associative too, the commutator of whose product is precisely the Hom-Lie product of the Hom-Lie central extension. Moreover, the algebra whose commutator realizes this Hom-Lie product is shown to be simple if the associated Lie algebra is nilpotent. Non-trivial examples are provided.
