可定义卷积与幂等Keisler测度 II
Definable convolution and idempotent Keisler measures II
AI总结：
该文研究NIP群中不变/有限可满足Keisler测度的卷积半群，刻画了极小左理想的结构，显式构造了非可定义顺从情形下的测度半群极小左理想，并分类了𝒢⁰⁰-不变幂等测度。
摘要：
我们研究NIP群中不变的/有限可满足的Keisler测度的卷积半群。我们证明理想（Ellis）子群始终是平凡的，并在可定义顺从的情形下刻画了极小左理想，证明它们总是构成Bauer单形。在一些假设下，我们从对应型半群中的极小左理想出发，显式构造了测度半群中的极小左理想（这包括SL₂(ℝ)的情形，该群不是可定义顺从的）。我们还证明典范前推映射是从𝒢上的可定义卷积到紧群𝒢/𝒢⁰⁰上经典卷积的同态，并利用它对𝒢⁰⁰-不变的幂等测度进行了分类。
英文摘要：
We study convolution semigroups of invariant/finitely satisfiable Keisler measures in NIP groups. We show that the ideal (Ellis) subgroups are always trivial and describe minimal left ideals in the definably amenable case, demonstrating that they always form a Bauer simplex. Under some assumptions, we give an explicit construction of a minimal left ideal in the semigroup of measures from a minimal left ideal in the corresponding semigroup of types (this includes the case of SL$_{2}(\mathbb{R})$, which is not definably amenable). We also show that the canonical push-forward map is a homomorphism from definable convolution on $\mathcal{G}$ to classical convolution on the compact group $\mathcal{G}/\mathcal{G}^{00}$, and use it to classify $\mathcal{G}^{00}$-invariant idempotent measures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
