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Topics in Cyclic Theory

BuchGebunden
328 Seiten
Englisch
Cambridge University Presserschienen am09.07.2020
Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988-92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.mehr
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Produkt

KlappentextNoncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988-92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.
Details
ISBN/GTIN978-1-108-47961-5
ProduktartBuch
EinbandartGebunden
FormatGenäht
Erscheinungsjahr2020
Erscheinungsdatum09.07.2020
Seiten328 Seiten
SpracheEnglisch
MasseBreite 193 mm, Höhe 231 mm, Dicke 23 mm
Gewicht544 g
Artikel-Nr.56056585

Inhalt/Kritik

Inhaltsverzeichnis
Introduction; 1. Background results; 2. Cyclic cocycles and basic operators; 3. Algebras of operators; 4. GNS algebra; 5. Geometrical examples; 6. The algebra of noncommutative differential forms; 7. Hodge decomposition and the Karoubi operator; 8. Connections; 9. Cocycles for a commutative algebra over a manifold; 10. Cyclic cochains; 11. Cyclic cohomology; 12. Periodic cyclic homology; References; List of symbols; Index of notation; Subject index.mehr

Autor

Daniel G. Quillen proved Adam's conjecture in topological K-theory, and Serre's conjecture that all projective modules over a polynomial ring are free. He was awarded the Cole Prize in Algebra and the Fields Medal in 1978. He was Waynflete Professor of Pure Mathematics at the University of Oxford, where he lectured on K-theory and cyclic homology.
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Quillen, Daniel G