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OverviewNoncommutative 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. Full Product DetailsAuthor: Daniel G. Quillen (University of Oxford) , Gordon Blower (Lancaster University)Publisher: Cambridge University Press Imprint: Cambridge University Press Dimensions: Width: 15.20cm , Height: 2.00cm , Length: 22.70cm Weight: 0.480kg ISBN: 9781108790444ISBN 10: 1108790445 Pages: 328 Publication Date: 09 July 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsIntroduction; 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.Reviews'The monograph is an excellent introduction to cyclic theory and an absolute must to any academic library, let alone a superb first-hand account and a selfless tribute to the late Daniel G. Quillen.' Igor V. Nikolaev, zbMATH Author InformationDaniel 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. Gordon Blower is Professor of Mathematical Analysis at Lancaster University, with interests in random matrices and applications of operator theory. He attended Quillen's lectures on cyclic theory when he was a junior researcher in Oxford. Tab Content 6Author Website:Countries AvailableAll regions |
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