- Additional chapter by Raedschelders and Van den Bergh surveys recent work that focuses on the representation theory of a number of bi- and Hopf algebras
- New edition of Manin's celebrated 1988 Montreal lectures
- Systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry
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- About this Textbook
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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.
- About the authors
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Yuri I. Manin is a Professor at the Max Planck Institute for Mathematics in Bonn. Personal distinctions include: Principal Researcher, Steklov Mathematical Institute, 1960-1993; since 1993 Principal Researcher in absentia. Professor (Algebra Chair), University of Moscow 1965-1992. Professor, M.I.T. 1992-1993. Scientific Member, MPI for Mathematics since 1993. Director, MPI for Mathematics 1995-2005, now Professor Emeritus. Board of Trustees Professor, Northwestern University (Evanston, USA) 2002-2011, now Professor Emeritus. Lenin Prize 1967. Brouwer Medal 1987. Frederic Esser Nemmers Prize 1994. Rolf Schock Prize in Mathematics 1999. King Faisal International Prize in Mathematics 2002. Georg Cantor Medal 2002. Order pour le Mérite for Science and Art, Germany, 2007. Great Cross of Merit with Star, Germany, 2008. János Bolyai International Mathematical Prize, Hungarian Academy of Sciences, 2010. Member of nine Academies of Sciences. Honorary degrees at Sorbonne, Oslo, Warwick. Honorary Member of the London Math. Society.
- Table of contents (16 chapters)
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Introduction
Pages 1-3
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The Quantum Group $${{\mathrm{GL}}}_q(2)$$
Pages 5-9
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Bialgebras and Hopf Algebras
Pages 11-17
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Quadratic Algebras as Quantum Linear Spaces
Pages 19-24
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Quantum Matrix Spaces. I. Categorical Viewpoint
Pages 25-28
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Table of contents (16 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Quantum Groups and Noncommutative Geometry
- Authors
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- Yuri I. Manin
- Series Title
- CRM Short Courses
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-97987-8
- DOI
- 10.1007/978-3-319-97987-8
- Hardcover ISBN
- 978-3-319-97986-1
- Series ISSN
- 2522-5200
- Edition Number
- 2
- Number of Pages
- VIII, 125
- Number of Illustrations
- 82 b/w illustrations, 1 illustrations in colour
- Additional Information
- Originally published by Centre de Recherches Mathématiques, Montreal, 1988
- Topics
