高阶阿贝尔幂幺作用的慢熵
Slow entropy of higher rank abelian unipotent actions
摘要：
研究了有限体积齐性空间$G/Γ$上阿贝尔幂幺作用$U$的慢熵不变量.对于每一个这样的行动，我们表明，拓扑慢熵可以直接从$\operatorname{Lie}(U)$诱导的$\operatorname{Lie}(G)$的一个特殊分解的维数计算。此外，我们能够证明，度量慢熵的行动符合其拓扑慢熵。作为推论，我们得到了任何交换素环作用的复杂性只与$G$的维数有关。这推广了[A. Kanigowski，K. Vinhage，D. Wei，Commun. 370（2019），第2期，449 - 474页。]更高等级的阿贝尔行为。
英文摘要：
We study slow entropy invariants for abelian unipotent actions $U$ on any finite volume homogeneous space $G/Γ$. For every such action we show that the topological slow entropy can be computed directly from the dimension of a special decomposition of $\operatorname{Lie}(G)$ induced by $\operatorname{Lie}(U)$. Moreover, we are able to show that the metric slow entropy of the action coincides with its topological slow entropy. As a corollary, we obtain that the complexity of any abelian horocyclic action is only related to the dimension of $G$. This generalizes the rank one results from [A. Kanigowski, K. Vinhage, D. Wei, Commun. Math. Phys. 370 (2019), no. 2, 449-474.] to higher rank abelian actions.
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。
