Let $G$ be an inductive limit of finite cyclic groups and let $A$ be a unitalsimple projectionless C*-algebra with $K_1(A) \cong G$ and with a uniquetracial state, as constructed based on dimension drop algebras by Jiang and Su.First, we show that any two aperiodic elements in $\Aut(A)/\WInn(A)$ areconjugate, where $\WInn(A)$ means the subgroup of $\Aut(A)$ consisting ofautomorphisms which are inner in the tracial representation. In the second part of this paper, we consider a class of unital simpleC*-algebras with a unique tracial state which contains the class of unitalsimple AT-algebras of real rank zero with a unique tracial state. This class isclosed under inductive limits and under crossed products by actions of $\Z$with the Rohlin property. Let $A$ be a TAF-algebra in this class. We show thatfor any automorphism $\alpha$ of $A$ there exists an automorphism$\widetilde{\alpha}$ of $A$ with the Rohlin property such that$\widetilde{\alpha}$ and $\alpha$ are asymptotically unitarily equivalent. Inits proof we use an aperiodic automorphism of the Jiang-Su algebra.
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机译:设$ G $为有限循环群的归纳极限,设$ A $为具有$ K_1(A)\ cong G $且具有唯一种族状态的简单无投影C *代数,这是根据Jiang的降维代数构造的首先,我们证明$ \ Aut(A)/ \ WInn(A)$中的任何两个非周期性元素都是共轭的,其中$ \ WInn(A)$表示$ \ Aut(A)$的子群由自同构组成,其中在种族代表中是内在的。在本文的第二部分中,我们考虑一类具有唯一tracial状态的单位单纯C *-代数,其中包含一类具有唯一tracial状态的实秩为零的unitalsimple AT-代数。通过Rohlin属性的$ \ Z $动作,在归纳极限和交叉乘积下封闭此类。假设$ A $是此类中的TAF代数。我们证明,对于任何自同构$ \ alpha $的$ A $,都存在具有Rohlin属性的自构$$ \ widetilde {\ alpha} $的Rohlin属性,使得$ \ widetilde {\ alpha} $和$ \ alpha $渐近equivalent等价的在证明中,我们使用了江苏代数的非周期自同构。
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