An introduction to C*-algebras and K-theory
This course offers an introductory exploration of the fundamental principles of $C^*$-algebras and $K$-theory with emphasis on classification of $C^*$-algebras using K-theoretic data. The first part of this course delves into the essential aspects of $C^$-algebras, which are helpful to introducing $K$-theory. These include the Gelfand representation, Gelfand-Naimark-Segal construction, and Gelfand-Naimark representation. The second part is devoted to the introduction of $K_0$-groups for $C^*$-algebras, covering their basic properties and exploring Elliott's classification of AF-algebras. Finally, the course proceeds to introduce $K_1$-groups.
讲师
日期
2023年09月18日 至 12月15日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周五 | 09:50 - 11:25 | A3-1a-205 | ZOOM 09 | 230 432 7880 | BIMSA |
修课要求
Undergraduate Functional Analysis, General Topology, Algebra
课程大纲
Fundamentals of the theory of $C^*$-algebras
Projections and unitaries
$K_0$-groups for unital $C^*$-algebras
$K_0$-groups for general $C^*$-algebras
Order structure of $K_0$-groups
Inductive limit $C^*$-algebras
Classification of AF-algebras
$K_1$-groups for $C^*$-algebras
Projections and unitaries
$K_0$-groups for unital $C^*$-algebras
$K_0$-groups for general $C^*$-algebras
Order structure of $K_0$-groups
Inductive limit $C^*$-algebras
Classification of AF-algebras
$K_1$-groups for $C^*$-algebras
参考资料
Gerard Murphy, $C^*$-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990. MR1074574 (91m:46084)
Mikael Rørdam, Flemming Larsen, and Niels Laustsen, An introduction to K-theory for $C^*$-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000. MR1783408 (2001g:46001)
Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
Mikael Rørdam, Flemming Larsen, and Niels Laustsen, An introduction to K-theory for $C^*$-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000. MR1783408 (2001g:46001)
Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
贺卓丰2018年毕业于东京大学，后成为该校副研究员。2022年华东师范大学博士后出站，2023年加入北京雁栖湖应用数学研究院任助理研究员。现在的研究兴趣包括C*代数的分类理论、C*动力系统和拓扑动力系统。