| 授業の目的 【日本語】 | | Title : K-theory for C*-algebras, and beyond
This course will provide an overview of some recent tools introduced at the crossroad between functional analysis, geometry and operator algebras. It can be considered as a course on non-commutative topology, which is the first step toward non-commutative geometry. In order to provide a large panorama on the subject together with applications, some details might be omitted, but references for all proofs will be provided. |
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| 授業の目的 【英語】 | | |
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| 到達目標 【日本語】 | | | Understand the basic notions of K-theory for C*-algebras. |
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| 到達目標 【英語】 | | |
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| 授業の内容や構成 | | C*-algebras
Projections and unitary elements
K_0 group for a unital C*-algebra
K_0 group for an arbitrary C*-algebra
The functor K_1
The index map
Higher K-functors, Bott periodicity
The six-term exact sequence
Cyclic cohomology
Applications |
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| 履修条件 | | | Knowledge on standard undergraduate linear algebra, calculus and advanced calculus. |
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| 関連する科目 | | | Any course on functional analysis and / or operator theory. This course will complement such courses, but they are not considered as prerequisite. |
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| 成績評価の方法と基準 | | | Grades based on attendance and on written reports. |
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| 教科書・テキスト | | | Lecture notes will be provided for this course. |
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| 参考書 | | Free reference books will be provided during the lectures, but first part of the course is mainly based on
An Introduction to K-theory for C*-algebras
from Rordam, Larsen and Laustsen.
More material will be available on
http://www.math.nagoya-u.ac.jp/~richard/Ktheorie.html
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| 課外学習等（授業時間外学習の指示） | | |
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| 注意事項 | | Additional information and material will be added regularly on
http://www.math.nagoya-u.ac.jp/~richard/Ktheorie.html |
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| 他学科聴講の可否 | | |
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| 他学科聴講の条件 | | | This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome. |
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| レベル | | |
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| キーワード | | | Hilbert space, self-adjoint operators, spectral theory, commutator methods. |
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| 履修の際のアドバイス | | | It is certainly easier to attend a course in English and to express yourself in this language in a quiet university environment rather than later on in a busy life. |
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| 授業開講形態等 | | |
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| 遠隔授業（オンデマンド型）で行う場合の追加措置 | | |
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