Diagonal-preserving gauge-invariant isomorphisms of graph C * -algebras
Diagonal-preserving gauge-invariant isomorphisms of graph C * -algebras
复制标题
图 C * -代数的保对角规范不变同构
DOI：
10.1016/j.jfa.2017.06.018
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发表时间：
2016
影响因子：
1.7
通讯作者：
James Rout
中科院分区：
文献类型：
--
作者：
T. M. Carlsen;James Rout
我们研究了具有广义规范作用的图C -代数，当两个图C -代数通过一个保持对角的同构交织在一起的广义规范作用而同构时，我们用群和群环来描述它们。我们应用这一特征来证明两个Cuntz-Krieger代数是同构的，当且仅当相应的单侧子移最终是共轭的，两个Cuntz-Krieger代数是同构的，当且仅当对应的双侧子移是共轭的，两个Cuntz-Krieger代数的稳定性是同构的，当且仅当对应的双侧子移是共轭的，两个Cuntz-Krieger代数是同构的，当且仅当对应的单侧子移是共轭的，两个Cuntz-Krieger代数是同构的，当且仅当对应的单侧子移是共轭的，两个Cuntz-Krieger代数的稳定性是同构的。
We study graph C⁎-algebras equipped with generalised gauge actions, and characterise in terms of groupoids and groupoid cocycles when two graph C⁎-algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the generalised gauge actions. We apply this characterisation to show that two Cuntz–Krieger algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the gauge actions if and only if the corresponding one-sided subshifts are eventually conjugate, and that the stabilisation of two Cuntz–Krieger algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the gauge actions if and only if the corresponding two-sided subshifts are conjugate.