Title: Rainbow Boomerang Graphs Show Chinese title

Title: 彩虹回旋镖图

Abstract: We generalize the well known exchange property of Coxeter groups to the setting of edge-colored graphs. This work aims to unify and extend the results of our companion article, "odd Verma's theorem", which were originally established for basic Lie superalgebras, to the broader setting of regular symmetrizable Kac-Moody Lie superalgebras and Nichols algebras of diagonal type, via the theory of Weyl groupoids in the sense of Heckenberger and Yamane. In particular, we show that the exchange property of odd reflections arises as a special case of the exchange property of Weyl groupoids. To study the exchange property itself, we analyze a class of edge-colored graphs introduced here, called rainbow boomerang graphs, which form an independently natural family of combinatorial objects. We also elaborate on odd Verma theorem in the specific setting of Nichols algebras of diagonal type. Show Chinese abstract

Abstract: 我们将Coxeter群的熟知的交换性质推广到带边彩色图的框架下。 本文旨在统一并扩展我们另一篇同行文章“奇Verma定理”的结果，该结果最初针对基本李超代数建立，通过Heckenberger和Yamane的Weyl广群理论，将其推广至更广泛的正则可对称化Kac-Moody李超代数以及对角型Nichols代数。 特别是，我们证明了奇反射的交换性质作为Weyl广群交换性质的一个特例出现。 为了研究交换性质本身，我们分析了一类在此引入的带边彩色图，称为彩虹回旋镖图，它们构成了一组独立的组合对象。 此外，我们还详细讨论了对角型Nichols代数背景下奇Verma定理的相关内容。