Extensions of C*-algebras

Huaxin Lin 林华新  (University of Oregon)

10:00-11:00, May 12, 2020   Zoom 677 6468 0474

Abstract:

C*-algebra extension theory began in 1970's. Its initial goal was to understand compact perturbation of normal operators on Hilbert space as well as essential normal operators. Brown-Douglas-Fillmore Theorem gave the first classification of essential normal operators up to approximate unitary equivalence using the essential spectra and Fredholm index. BDF-theory quickly evolved into the study of extensions of C*-algebras of continuous functions on a compact metric space by the algebra of compact operators. Kasparov's KK-theory was developed based on BDF-theory which led to a completely new board territory of mathematics. However, KK-theory is a stably theory and more than often C*-algebra extension theory is not. In this talk, we will present some new results about C*-algebra extension theory with a small simple ideal like the algebra of compact operators.

About the speaker:

林华新，华东师范大学紫江讲座教授，美国数学会首届会士。2005年获上海市科学技术进步一等奖。主要从事算子代数的研究。90年代解决了矩阵论中长期未决的Halmos问题。2000年以后引入并发展了在C*-代数分类中起着核心作用的迹秩理论，独立证明了迹秩有限C*-代数的分类定理，首次基于简单抽象结构做出广泛的C*-代数分类，推动了整个C*-代数理论的发展。2014年以来，与他人合作取得重大进展，实现了对Z-稳定的可分单核幺C*-代数的完全分类，从而完成了C*-代数领域中著名的“Elliott 纲领”。被邀请在1997年欧盟算子代数大会、2014年国际数学家大会 (ICM) 算子代数卫星会议上作大会报告。2015年受CBMS、AMS和NSF联合特别邀请作十场系列讲座。

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