Quantum groups and noncommutative geometry

書誌事項

Quantum groups and noncommutative geometry

Yuri I. Manin

(CRM short courses)

Springer , Centre de Recherches Mathématiques, c2018

2nd ed. / with a contribution by Theo Raedschelders and Michel Van den Bergh

  • : pbk.

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注記

Includes bibliographical references (p. 117-121) and index

内容説明・目次

内容説明

This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka-Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.

目次

1. The Quantum Group GL(2).- 2. Bialgebras and Hopf Algebras.- 3. Quadratic Algebras as Quantum Linear Spaces.- 4. Quantum Matrix Spaces. I. Categorical Viewpoint.- 5. Quantum Matrix Spaces. II. Coordinate Approach.- 6. Adding Missing Relations.- 7. From Semigroups to Groups.- 8. Frobenius Algebras and the Quantum Determinant.- 9. Koszul Complexes and the Growth Rate of Quadratic Algebras.- 10. Hopf *-Algebras and Compact Matrix Pseudogroups.- 11. Yang-Baxter Equations.- 12. Algebras in Tensor Categories and Yang-Baxter Functors.- 13. Some Open Problems.- 14. The Tannaka-Krein Formalism and (Re)Presentations of Universal Quantum Groups.- Bibliography.- Index.

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詳細情報

  • NII書誌ID(NCID)
    BB27217999
  • ISBN
    • 9783319979861
    • 9783030074326
  • LCCN
    2018950779
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    [Cham],[Montréal]
  • ページ数/冊数
    vii, 125 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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