论文标题
Frobenius von Neumann代数的量子卷积不平等
Quantum convolution inequalities on Frobenius von Neumann algebras
论文作者
论文摘要
在本文中，我们介绍了Frobenius von Neumann代数并研究量子卷积的不平等。在此框架中，我们统一了量子杨对量子对称器（例如亚因子）的不平等，以及在量子傅立叶分析中研究的融合双向骨架。此外，我们证明了量子熵卷积的不平等，并在亚因子情况下表征了极端变化。我们还证明了量子平滑的熵卷积不平等。我们获得了亚比例平面代数的积极性，该代数比量子schur乘积定理强。所有这些不平等都提供了比Schur产品标准更强的融合环分类的分析障碍。
In this paper, we introduce Frobenius von Neumann algebras and study quantum convolution inequalities. In this framework, we unify quantum Young's inequality on quantum symmetries such as subfactors, and fusion bi-algebras studied in quantum Fourier analysis. Moreover, we prove quantum entropic convolution inequalities and characterize the extremizers in the subfactor case. We also prove quantum smooth entropic convolution inequalities. We obtain the positivity of comultiplications of subfactor planar algebras, which is stronger than the quantum Schur product theorem. All these inequalities provide analytic obstructions of unitary categorification of fusion rings stronger than Schur product criterion.
