An Introduction to C-Algebras and Noncommutative Geometry / / by Heath Emerson

• Autore: Emerson Heath
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2024
• Edizione: 1st ed. 2024.
• Descrizione fisica: 1 online resource (548 pages)
• Disciplina: 512.55
• Soggetto topico: 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)
• Soggetto genere / forma: Llibres electrònics
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: -Algebras and Noncommutative Geometry
• ISBN: 9783031598500; 9783031598494
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910878058803321
• Lo trovi qui: Univ. Federico II
• Serie: Birkhäuser Advanced Texts Basler Lehrbücher, . 2296-4894