论文标题
root groupoid及相关谎言超级
Root groupoid and related Lie superalgebras
论文作者
论文摘要
我们引入了一个根类固醇的概念，以替代Weyl群（Kac-Moody）的概念。 root groupoid的对象对某些根数据进行了分类，箭头由生成器和关系定义。作为一个抽象的群体，root groupoid具有许多连接的组件，我们表明其中一些人可以将一个有趣的谎言级级别的家族联系起来，我们称之为root superalgebras。我们对满足一些其他假设的根部超级分类进行了分类。对于每个root groupoid组件，我们将一个图形（称为骨骼）关联到Weyl组的Cayley图。我们以这种方式建立了骨骼概括的Coxeter特性，即Kac-Moody Lie代数是Coxeter的事实。
We introduce a notion of a root groupoid as a replacement of the notion of Weyl group for (Kac-Moody) Lie superalgebras. The objects of the root groupoid classify certain root data, the arrows are defined by generators and relations. As an abstract groupoid the root groupoid has many connected components and we show that to some of them one can associate an interesting family of Lie superalgebras which we call root superalgebras. We classify root superalgebras satisfying some additional assumptions. To each root groupoid component we associate a graph (called skeleton) generalizing the Cayley graph of the Weyl group. We establish the Coxeter property of the skeleton generalizing in this way the fact that the Weyl group of a Kac-Moody Lie algebra is Coxeter.
