Topics in cyclic theory / Daniel G. Quillen and Gordon Blower.

Format:

Book

Author/Creator:

Quillen, Daniel G., author.

Blower, G. (Gordon), author.

Series:

London Mathematical Society student texts ; 97.

London Mathematical Society student texts ; 97

Language:

English

Subjects (All):

Algebraic cycles.

Physical Description:

x, 320 pages : illustrations (black and white) ; 24 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, [2020]

Summary:

"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."- publisher

Contents:

Background result

Cyclic cocycles and basic operators

Algebras of operators

GNS algebra

Geometrical examples

The algebra of noncommutative differential forms

Hodge decomposition and the Karoubi operator

Connections

Cocycles for a commutative algebra over a manifold

Cyclic cohomology.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Quillen, Daniel G. Topics in cyclic theory

ISBN:

9781108479615

1108479618

9781108790444

1108790445

OCLC:

1150949732