主持人：王航 教授
报告简介：Based on previous results on ideals in reduced groupoid C*-algebras, Christian B?nicke and I proved in 2018 that all ideals in a reduced groupoid C*-algebra C_r*(G) are dynamical if and only if the underlying étale groupoid G is inner exact and has the residual intersection property. Recall that an ideal I in the reduced groupoid C*-algebra C_r*(G) is dynamical if I is uniquely determined by an open invariant subset U of the unit space G^0 of the groupoid G. Equivalently, I is the ideal generated by C_0(U) inside C_r*(G). In the joint work with Jiawen Zhang, we are investigating ideals in reduced C*-algebras of general étale groupoids. Generally, each ideal I in C_r*(G) is associated with two open invariant subsets of G^0, called the inner support U_I and the outer support V_I for the given ideal I. By introducing the notion of ghostly ideals in C_r*(G), we are able to extend the sandwiching result for ideals in C_r*(G) from inner exact groupoids to general groupoids. Moreover, we use effectiveness and the intersection property to characterize when the inner and outer supports of a given ideal in C_r*(G) coincide. Finally, we provide several applications to regular ideals, tracial ideals and amenability problem for the Thompson's group F. In this lecture, I will first explain the basic properties for étale groupoids and describe some key classes of examples including transformation groupoids and coarse groupoids. Then, I will introduce the inner and outer supports of a given ideal I in C_r*(G) and characterise when the inner and outer supports of I coincide via the effectiveness and the intersection property. The main tool for the proof is the revised sandwiching result for the ideal structure of C_r*(G).
主讲人简介：李康，丹麦青年数学家，德国纽伦堡大学教授，专长于算子代数及其在动力系统、几何群论与表示论中的应用，在IMRN, JFA, Adv Math, Ergodic Theory Dynam. Systems，JNCG发表近30篇论文。
