图C*-代数的最大置换对称性的量子对称性
算子代数
2025-04-22 v4
摘要
过去几年中，多个数学家在不同范畴中探讨了图 -代数 对应的量子对称性。在本文中，我们证明恰好存在三族紧矩阵量子群，包含对应于底图 边集合上的对称群，能够作为图 -代数在由Joardar和Mandal引入的范畴中实现的量子对称性。此外，我们展示，对于一个没有孤立顶点的有限图 ，若 为其 的量子自同构群，则 必为标量矩阵。
引用
@article{arxiv.2406.13484,
title = {Quantum Symmetries of Graph C*-algebras Having Maximal Permutational Symmetry},
author = {Ujjal Karmakar and Arnab Mandal},
journal= {arXiv preprint arXiv:2406.13484},
year = {2025}
}
备注
The article will appear in the International Journal of Mathematics. It was previously titled "Unitary Easy Quantum Groups Arising as Quantum Symmetries of Graph C*-algebras", but the title has been changed based on the referee's suggestion. The introduction and preliminaries have been shortened, and the statements of the lemmas, propositions in the main section have been revised for clarity