论文标题
Künneth分裂和与许多理想有限的C* - 代数分类
Künneth Splittings and Classification of C*-Algebras with Finitely Many Ideals
论文作者
论文摘要
真实等级零的AD代数类别由具有系数的精确k组序列进行分类，该系数配备了某些阶构建结构。这样的序列总是被拆分的，因此可能会问为什么中间组与分类有关。答案是，不一定总是选择分裂图来尊重所涉及的顺序结构。 这可以根据相关代数的理想来改写。我们证明，当C*-Algebra只有有限的理想时，尊重这些理想的图表始终存在。因此，真实等级为零的AD代数有限的许多理想是通过（经典）有序的K理论归类的。我们还指出了这些方法如何概括为具有缓慢尺寸增长和实际等级零的整个灰分代数。
The class of AD algebras of real rank zero is classified by an exact sequence of K-groups with coefficients, equipped with certain order structures. Such a sequence is always split, and one may ask why, then, the middle group is relevant for classification. The answer is that the splitting map can not always be chosen to respect the order structures involved. This may be rephrased in terms of the ideals of the C*-algebras in question. We prove that when the C*-algebra has only finitely many ideals, a splitting map respecting these always exists. Hence AD algebras of real rank zero with finitely many ideals are classified by (classical) ordered K-theory. We also indicate how the methods generalize to the full class of ASH algebras with slow dimension growth and real rank zero.
