江苏建设概述
A generalization of the Jiang-Su construction
摘要：
设$G$是可数阿贝尔群.构造了一个具有唯一迹态的单无投影C*-代数$A$，它满足$(K_0(A), [1_A]) \cong (\Z, 1) $，$K_1(A) \cong G$，张量地吸收了Jiang-Su代数，并作为一个特定形式的降维代数序列的归纳极限C* 代数.这种构造是在江苏代数构造的基础上进行的。通过这种构造，我们给出了无投影C* 代数的非周期自同构的共轭性结果。证明了无投影C*-代数的自同构具有一定的非周期性，直到迹表示中的弱内自同构为止当且仅当它具有一种Rohlin性质，从而得到了某些实秩为零的C* 代数的张量积的Rohlin性质.
英文摘要：
Let $G$ be a countable abelian group. We construct a unital simple projectionless C*-algebra $A$ with a unique tracial state, that satisfies $(K_0(A), [1_A]) \cong (\Z, 1) $, $K_1(A) \cong G$, absorbs the Jiang-Su algebra tensorially, and that is obtained as the inductive limit C*-algebra of a sequence of dimension drop algebras of a specific form. This construction is based on the construction of the Jiang-Su algebra. By this construction, we show a certain conjugacy result for aperiodic automorphisms of these projectionless C*-algebras. We also show that an automorphism of this projectoinless C*-algebra has a certain aperiodicity up to the weakly inner automorphisms in the tracial representation if and only if it has a kind of Rohlin property, which leads to the Rohlin property after taking tensor product of certain C*-algebras of real rank zero.
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