Villadsen代数的正则性及其中心序列代数的特征标
Regularity of Villadsen algebras and characters on their central sequence algebras
摘要：
证明了：如果A是种子空间为有限维CW复形的第一类单Villadsen代数，或A是第二类单Villadsen代数，则$A$张量吸收Jiang-Su代数当且仅当A的中心序列代数不允许特征标.此外，在与Joan Bosa的联合附录中，我们证明了具有无限稳定秩的第二类Villadsen代数不具有Corona分解性质，从而提供了具有唯一迹态的单可分核$C^\ast$ -代数不具有该性质的第一个例子。
英文摘要：
We show that if A is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then $A$ absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of A does not admit characters. Additionally, in a joint appendix with Joan Bosa, we show that the Villadsen algebra of the second type with infinite stable rank fails the Corona Factorization Property, thus providing the first example of a unital, simple, separable and nuclear $C^\ast$-algebra with a unique tracial state which fails to have this property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
