标题： 幺正表示的熵概念 显示英文标题

标题： Notions of entropy for unitary representations

摘要： 在过去二十年中，Lewis Bowen的sofic熵及其退火版本（最初称为“f-不变量”）在非换群作用的遍历理论中占据了中心地位。 在这项工作中，我们沿着遍历理论与表示理论之间的类比继续探讨这些熵的概念。 我们得到了与群的酉表示和其他C*-代数的表示相关的新量。 我们发现了与算子理论中的经典构造以及独立随机酉矩阵组的研究之间的联系。 显示英文摘要

摘要： In the last twenty years, Lewis Bowen's sofic entropy and its annealed version (originally called the `f-invariant') have taken a central place in the ergodic theory of actions of non-amenable groups. In this work we pursue these notions of entropy across the analogy between ergodic theory and representation theory. We arrive at new quantities associated to unitary representations of groups and representations of other C*-algebras. We find connections to both classical constructs in operator theory and the study of tuples of independent random unitary matrices.