平稳 AF-代数及其相伴有序单维数群的同构问题的可判定性
算子代数
2007-05-23 v3 动力系统
摘要
本文考虑稳定 AF-C*-代数的同构概念在相应 Bratteli 图为平稳的情形，即与单个平方本原非奇异关联矩阵相伴的情形。C*-同构在这些矩阵上诱导出一个称为 C*-等价的等价关系。我们证明相伴的同构等价问题是可判定的，即存在一个算法，可用于在有限步内检验两个给定的本原非奇异矩阵是否 C*-等价。
引用
@article{arxiv.math/9910103,
title = {Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups},
author = {Ola Bratteli and Palle E. T. Jorgensen and Ki Hang Kim and Fred Roush},
journal= {arXiv preprint arXiv:math/9910103},
year = {2007}
}
备注
55 pages, LaTeX2e (amsart class). In this version the main theorem has been extended to possibly singular primitive integer matrixes, and the clarity of the presentation has been improved substantially throughout the paper