熵与单位元表示的行列式
Entropy and determinants for unitary representations
AI总结：
本文通过类比遍历论与表示论，提出新的单位元表示和C*-代数表示的熵量，这些量可计算为Fuglede-Kadison行列式，扩展了Szegő定理，并联系了子对角子代数理论和紧Abel群自同构的遍历论。
摘要：
遍历论中包含几种概率保持动作的熵概念，如Kolmogorov-Sinai熵基于Følner序列的可算群，基于随机排列的熵，以及Bowen的sofic熵。本文通过遍历论与表示论的类比，提出新的单位元表示和C*-代数表示的熵量，这些量可计算为Fuglede-Kadison行列式。所得行列式公式提供了Szegő定理的非交换推广，并与Arveson的子对角子代数理论以及紧Abel群自同构的遍历论中的熵公式相联系。
英文摘要：
Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on Følner sequences for amenable groups, entropy defined using a random ordering of the group, and Bowen's sofic entropy for sofic groups. In this work we pursue these notions across an analogy between ergodic theory and representation theory. We arrive at new quantities associated to unitary representations of groups and representations of other C*-algebras. Our main results show that these new quantities can often be evaluated as Fuglede--Kadison determinants. The resulting determinantal formulas offer various non-commutative generalizations of Szegő's limit theorem for Toeplitz determinants. They make contact with Arveson's theory of subdiagonal subalgebras, and also with some entropy formulas in the ergodic theory of actions by automorphisms of compact Abelian groups.
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。
