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Record Nr. |
UNINA9910878058803321 |
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Autore |
Emerson Heath |
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Titolo |
An Introduction to C-Algebras and Noncommutative Geometry / / by Heath Emerson |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2024 |
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ISBN |
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9783031598500 |
9783031598494 |
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Edizione |
[1st ed. 2024.] |
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Descrizione fisica |
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1 online resource (548 pages) |
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Collana |
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Birkhäuser Advanced Texts Basler Lehrbücher, , 2296-4894 |
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Disciplina |
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Soggetti |
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K-theory |
Topology |
Geometry, Differential |
Dynamics |
Functional analysis |
K-Theory |
Differential Geometry |
Dynamical Systems |
Functional Analysis |
C*-àlgebres |
Geometria diferencial no commutativa |
Teoria espectral (Matemàtica) |
K-teoria |
Teoria de l'índex (Matemàtica) |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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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 |
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Noncommutative Geometry -- An Introduction to KK-theory -- Bibliography. |
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Sommario/riassunto |
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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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