标题： 倒数Cuntz--Krieger代数 显示英文标题

标题： Reciprocal Cuntz--Krieger algebras

摘要： Kirchberg代数中的互反性是强扩张群与K理论群之间的对偶性。 我们描述了一个构造，通过扩张的K理论对偶性，构造了具有有限生成K群的Kirchberg代数$\mathcal{A}$的互反对偶代数$\widehat{\mathcal{A}}$。 特别是，我们可以具体实现简单Cuntz--Krieger代数$\mathcal{O}_A$的互反代数$\widehat{\mathcal{O}}_A$。 作为结果，代数$\widehat{\mathcal{O}}_A$被实现为由满足某些算子关系的部分等距构成的族生成的单位化简单纯无限通用$C^*$-代数。 我们将研究倒代数$\widehat{\mathcal{O}}_A$上的规范作用，并证明存在一个同构，将基本群$\pi_1({\operatorname{Aut}}({\mathcal{O}}_A))$和$\pi_1({\operatorname{Aut}}(\widehat{\mathcal{O}}_A))$联系起来，同时保留它们的规范作用。 显示英文摘要

摘要： Reciprocality in Kirchberg algebras is a duality between strong extension groups and K-theory groups. We describe a construction of the reciprocal dual algebra $\widehat{\mathcal{A}}$ for a Kirchberg algebra $\mathcal{A}$ with finitely generated K-groups via K-theoretic duality for extensions. In particular, we may concretely realize the reciprocal algebra $\widehat{\mathcal{O}}_A$ for simple Cuntz--Krieger algebras $\mathcal{O}_A$. As a result, the algebra $\widehat{\mathcal{O}}_A$ is realized as a unital simple purely infinite universal $C^*$-algebra generated by a family of partial isometries subject to certain operator relations. We will also study gauge actions on the reciprocal algebra $\widehat{\mathcal{O}}_A$ and prove that there exists an isomorphism between the fundamental groups $\pi_1({\operatorname{Aut}}({\mathcal{O}}_A))$ and $\pi_1({\operatorname{Aut}}(\widehat{\mathcal{O}}_A))$ preserving their gauge actions.