与有限对齐高阶图相关的扭曲相对Cuntz-Krieger代数
算子代数
2013-10-29 v1
摘要
对于每个有限对齐的高阶图 和 上的每个 值2上循环，我们关联一族扭曲相对Cuntz-Krieger代数。我们证明这些代数中的每一个都带有规范作用，并证明了一个规范不变唯一性定理。我们描述了扭曲和未扭曲相对Cuntz-Krieger代数上规范作用的不动点代数之间的同构。我们证明扭曲相对Cuntz-Krieger代数关于规范不变理想的商典范地同构于与子图相关的扭曲相对Cuntz-Krieger代数。我们利用这一点提供了每个扭曲相对Cuntz-Krieger代数的规范不变理想结构的完整图论描述。
引用
@article{arxiv.1310.7045,
title = {Twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs},
author = {Benjamin Whitehead},
journal= {arXiv preprint arXiv:1310.7045},
year = {2013}
}
备注
Author's honours thesis submitted to the University of Wollongong in 2012. Many of the results in this thesis will appear in the paper 'Twisted C*-algebras associated to finitely aligned higher-rank graphs' by A. Sims, B. Whitehead and M. Whittaker. As the calculations in this thesis are given in greater detail than in the paper, the full details are made available here for reference. 114 pages