讲座题目：Irreducible inclusions of simple C*-algebras 主讲人：Mikael Rordam 教授 主持人：王勤 教授 开始时间：2022-08-04 15:30 讲座地址：Zoom Meeting ID: 878 9000 0739 Passcode: 416548 主办单位：数学科学学院
报告人简介： Mikael Rørdam教授是丹麦皇家科学院院士、丹麦国家数学委员会主席、哥本哈根大学数学系科研副主任、国际Ostrowski奖评委，国际算子代数研究领域的领军人物。Rørdam教授长期致力于算子代数、动力系统、几何群论、K-理论等领域的研究，尤其在Elliott猜测方面取得重要成果，其研究成果发表在Annals of Mathematics, Acta Mathematica等顶尖的数学杂志上，文章总引用率达2800多次。由于在C*-代数的结构和分类理论中的卓越工作，2006年，Rørdam教授应邀在马德里召开的第25届国际数学家大会（ICM）上作特邀报告。
报告内容： There are several naturally occurring interesting examples of inclusions of simple C*-algebras with the property that all intermediate C*-algebras likewise are simple. Moreover, in many cases one even has a Galois type classification of intermediate C*-algebras of such inclusions. By analogy with von Neumann algebras, we refer to such inclusions as being C*-irreducible. We give an intrinsic characterization of C*-irreducible inclusions, and use this characterization to exhibit (and revisit) such inclusions, both known ones and new ones, arising from groups and dynamical systems. In a recent joint work with Echterhoff we show when inclusions of the form $A^H \subseteq A \rtimes G$ are C*-irreducible, where G and H are groups acting on a C*-algebra A, and use this to exhibit new C*-irreducible inclusions with interesting properties. We explore an averaging technique introduced by Popa and show how this can be used both to prove irreducibility of certain inclusions arising from crossed products and to establish a classification of their intermediate C*-algebras. |
