Farah Ilijas, Hirshberg Ilan
Department of Mathematics and Statistics, York University, North York, ON M3J 1P3, Canada;
Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva 84105, Israel.
Proc Natl Acad Sci U S A. 2017 Jun 13;114(24):6244-6249. doi: 10.1073/pnas.1619936114. Epub 2017 May 30.
We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable [Formula: see text]-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra [Formula: see text] or of the canonical anticommutation relations (CAR) algebra.
我们证明，与带有选择公理的策梅洛 - 弗兰克尔集合论（ZFC）一致的是，存在一个简单核非可分(C^*) - 代数，它与它的对合代数不同构。此外，我们可以保证这个例子是康茨代数(\mathcal{O}_n)的幺正副本或典范反对易关系（CAR）代数的归纳极限。
