書誌事項

Topics in cyclic theory

Daniel G. Quillen and Gordon Blower

(London Mathematical Society student texts, 97)

Cambridge University Press, 2020

  • : hardback

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注記

Includes bibliographical references (p. 307-311) and index

内容説明・目次

内容説明

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.

目次

  • 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.

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詳細情報

  • NII書誌ID(NCID)
    BB31576984
  • ISBN
    • 9781108479615
  • LCCN
    2020012378
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    x, 320 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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