Quantum convolution inequalities on Frobenius von Neumann algebras  

作　　者：Linzhe Huang Zhengwei Liu Jinsong Wu 

机构地区：[1]Beijing Institute of Mathematical Sciences and Applications,Beijing 101408,China [2]Yau Mathematical Sciences Center and Department of Mathematics,Tsinghua University,Beijing100084,China

出　　处：《Science China Mathematics》2025年第3期615-636,共22页中国科学(数学英文版)

基　　金：supported by Beijing Municipal Science&Technology Commission,Administrative Commission of Zhongguancun Science Park(Grant No.Z221100002722017);supported by grants from Beijing Institute of Mathematical Sciences and Applications;supported by China’s National Key R&D Programmes(Grant No.2020YFA0713000);Tsinghua University(Grant No.04200100122);Templeton Religion Trust(TRT 159);supported by Beijing Natural Science Foundation Key Program(Grant No.Z220002);supported by National Natural Science Foundation of China(Grant Nos.12031004 and 12371124)。

摘　　要：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 the Schur product criterion.

关 键 词：Frobenius von Neumann algebra quantum Young's inequality quantum entropic convolution inequality unitary categorification 

分 类 号：O178[理学—数学]