发表机构
UNSW Sydney; University of Wollongong; Université de Lorraine（新南威尔士大学; 伍伦贡大学; 洛林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入紧半单李群的晶体群胚，证明其代数和轨道空间分别实现晶体极限和Weyl群，并推广至旗流形。
AI 中文摘要
我们引入了紧半单李群 $K$ 的晶体群胚；它是Kashiwara晶体逆极限上有限型子位移的高秩类比物的Deaconu-Renault群胚。我们证明其Steinberg代数和$C^*$-代数分别实现了$K$的多项式函数代数的晶体极限及其$C^*$-包络，这是Matassa和本文第二作者意义上的。我们证明晶体群胚的轨道空间与$K$的Weyl群双射，其拓扑由Weyl群上的Bruhat序决定。我们还为旗流形及相关的Poisson齐性空间定义了晶体群胚，并证明了类似的结构结果。
英文摘要
We introduce the crystal groupoid of a compact semisimple Lie group $K$; it is the Deaconu-Renault groupoid of a higher-rank analogue of a subshift of finite type on an inverse limit of Kashiwara crystals. We show that its Steinberg algebra and its $C^*$-algebra realise the crystal limits of the polynomial function algebra of $K$ and its $C^*$-envelope, respectively, in the sense of Matassa and the second author. We show that the orbit space of the crystal groupoid is in bijection with the Weyl group of $K$, with topology determined by the Bruhat order on the Weyl group. We also define a crystal groupoid for flag manifolds and related Poisson homogeneous spaces, and prove the analogous structural results.
