Title: Invariant measures on the transversal hull of cone semigroups and some applications Show Chinese title

Title: 锥半群横截壳上的不变测度及其一些应用

Abstract: Let $\LL_{\bf v}\subset \Z^D$ be a suitable cone semigroup and $\A_{\bf v}$ its reduced semigroup $C^*$-algebra. In this paper, we compute the $\LL_{\bf v}$-invariant measures in the transversal hull of the semigroup $\LL_{\bf v}$ that exhibit regularity in the boundaries of $\LL_{\bf v}.$ These measures enable the construction of a trace per-unit hypersurface for observables in $\A_{\bf v}$ supported near the boundaries of $\LL_{\bf v}$, leading to the construction of appropriate Chern cocycles in the "boundary" ideals of $\A_{\bf v}$. Our approach applies to both finitely and non-finitely generated cone semigroups. Applications for the bulk-defect correspondence of lattice models of topological insulators are also provided. Show Chinese abstract

Abstract: 设 $\LL_{\bf v}\subset \Z^D$ 是一个合适的锥半群， $\A_{\bf v}$ 是其约化半群 $C^*$-代数。 在本文中，我们计算了半群$\LL_{\bf v}$的横截壳中具有$\LL_{\bf v}$不变性的测度，这些测度在$\LL_{\bf v}.$的边界上表现出规律性。这些测度使得可以在$\A_{\bf v}$中构造单位超曲面的迹，这些可观测量在$\LL_{\bf v}$的边界附近支持，从而在$\A_{\bf v}$的“边界”理想中构造适当的陈类上循环。我们的方法适用于有限生成和非有限生成的锥半群。还提供了用于拓扑绝缘体格点模型的体-缺陷对应的应用。