An Introduction to C*-Algebras and Noncommutative Geometry
This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a...
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| Format: | Electronisk eBog |
| Sprog: | engelsk |
| Udgivet: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2024.
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| Udgivelse: | 1st ed. 2024. |
| Serier: | Birkhäuser Advanced Texts Basler Lehrbücher,
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| Fag: | |
| Online adgang: | https://doi.org/10.1007/978-3-031-59850-0 |
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| Summary: | This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes’ Noncommuntative Riemannian geometry. Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details. |
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| Fysisk beskrivelse: | 1 online resource (XIII, 539 p. 27 illus.). |
| ISBN: | 9783031598500 |
| ISSN: | 2296-4894 |
| DOI: | 10.1007/978-3-031-59850-0 |