论文标题
可定义的卷积和愿意的keisler措施II
Definable convolution and idempotent Keisler measures II
论文作者
论文摘要
我们研究了NIP组中不变/有限令人满意的Keisler度量的卷积半群。我们表明，理想的（Ellis）亚组总是微不足道的，并在明确的情况下描述了最小的左左理想，这表明它们总是形成鲍尔单纯形。在某些假设下，我们从相应类型的相应半群中的最小左左理想中给出了最小左左理想的明确构造（这包括Sl $ _ {2}（\ Mathbb {r}）$的sl $ _ {2}（\ Mathbb {r}）$，这绝对是不可弥补的）。我们还表明，规范推向前向图是从$ \ Mathcal {g} $上定义的卷积到紧凑型组$ \ MATHCAL {G}/\ MATHCAL {g}^{g}^{00} $的经典卷积的同态同性形态，并使用它来分类$ \ nathcal unccal rescal rescal {g} g}^$}
We study convolution semigroups of invariant/finitely satisfiable Keisler measures in NIP groups. We show that the ideal (Ellis) subgroups are always trivial and describe minimal left ideals in the definably amenable case, demonstrating that they always form a Bauer simplex. Under some assumptions, we give an explicit construction of a minimal left ideal in the semigroup of measures from a minimal left ideal in the corresponding semigroup of types (this includes the case of SL$_{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.
