Quantum Groups and Noncommutative Geometry
2nd Edition
Published on 11. October 2018
VIII, 125 pages
978-3-319-97987-8 (ISBN)
Description
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.
More details
Series
Edition
Second Edition 2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
VIII, 125 p. 83 illus., 1 illus. in color.
File size
2,27 MB
ISBN-13
978-3-319-97987-8 (9783319979878)
DOI
10.1007/978-3-319-97987-8
Schweitzer Classification
Other editions
Additional editions
Yuri I. Manin
Quantum Groups and Noncommutative Geometry
With a Contribution by Theo Raedschelders and MIchel Van den Brgh
Book
10/2018
2nd Edition
Springer
€64.19
Shipment within 10-15 days
Persons
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.
Content
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.
