An introduction to C*-algebras and noncommutative geometry / Heath Emerson.
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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Full Text (via Springer) |
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| Format: | eBook |
| Language: | English |
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Cham :
Birkhäuser,
[2024]
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| Series: | Birkhäuser advanced texts.
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MARC
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| 245 | 1 | 3 | |a An introduction to C*-algebras and noncommutative geometry / |c Heath Emerson. |
| 264 | 1 | |a Cham : |b Birkhäuser, |c [2024] | |
| 264 | 4 | |c ©2024 | |
| 300 | |a 1 online resource (xiii, 539 pages) : |b illustrations. | ||
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| 490 | 1 | |a Birkhäuser advanced texts Basler Lehrbücher, |x 2296-4894 | |
| 504 | |a Includes bibliographical references. | ||
| 520 | |a 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. | ||
| 505 | 0 | |a An introduction to C*-algebras -- An Introduction to Index Theory and Noncommutative Geometry -- Spectral Theory and Representation -- Positivity, Representations, Tensor Products and Ideals in C*-algebras -- Module theory of C*-algebras -- Morita Equivalence -- Topological K-theory and Clifford Algebras -- K-theory for C*algebras -- The Index Theorem of Atiyah and Singer -- K-homology and Noncommutative Geometry -- An Introduction to KK-theory -- Bibliography. | |
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed August 1, 2024). | |
| 650 | 0 | |a C*-algebras. |0 http://id.loc.gov/authorities/subjects/sh85018534 | |
| 650 | 0 | |a Noncommutative differential geometry. |0 http://id.loc.gov/authorities/subjects/sh97004788 | |
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