论文标题
k的二元性二元性用于cuntz-krieger代数的扩展
K-theoretic duality for extensions of Cuntz-Krieger algebras
论文作者
论文摘要
我们通过使用k-词素长的精确序列和循环六个项精确序列的k理论群体来介绍了可分离的Unital核$ C^*$ - 代数的扩展的K理论二元性的概念。然后，我们证明了cuntz-krieger代数的toeplitz扩展$ \ MATHCAL {O} _ {a^t} $用于$ a $的转移矩阵$ a^t $。一对同构cuntz - krieger代理$ \ nathcal {o} _a $和$ \ nathcal {o} _b $不一定会产生$ \ nathcal {o} _ {o} _ {a^t} $ and $ \ m nai的同构的同构，并显示了一对两个toeplitz代数$ \ MATHCAL {t} _a $和$ \ MATHCAL {t} _b $在且仅当toeplitz代数$ \ MATHCAL {T} _ {a^a^a^a^a^a^b} $和$ {a^$ c {转置矩阵是同构的。
We introduce the notion of K-theoretic duality for extensions of separable unital nuclear $C^*$-algebras by using K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the Toeplitz extension $\mathcal{T}_A$ of a Cuntz-Krieger algebra $\mathcal{O}_A$ is the K-theoretic dual of the Toeplitz extension $\mathcal{T}_{A^t}$ of the Cuntz-Krieger algebra $\mathcal{O}_{A^t}$ for the transposed matrix $A^t$ of $A$. A pair of isomorphic Cuntz--Krieger algebras $\mathcal{O}_A$ and $\mathcal{O}_B$ does not necessarily yield the isomorphic pair of $\mathcal{O}_{A^t}$ and $\mathcal{O}_{B^t}.$ However, as an application, we may show that two Toeplitz algebras $\mathcal{T}_A$ and $\mathcal{T}_B$ are isomorphic as $C^*$-algebras if and only if the Toeplitz algebras $\mathcal{T}_{A^t}$ and $\mathcal{T}_{B^t}$ of their transposed matrices are isomorphic.
