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Quantum Groups and Noncommutative Geometry de Yuri I. Manin

Quantum Groups and Noncommutative Geometry: CRM Short Courses

Autor Yuri I. Manin Contribuţii de Theo Raedschelders, Michel Van den Bergh
en Limba Engleză Hardback – 22 oct 2018
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.
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Specificații

ISBN-13: 9783319979861
ISBN-10: 3319979868
Pagini: 124
Ilustrații: VIII, 125 p. 83 illus., 1 illus. in color.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.45 kg
Ediția:2nd ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria CRM Short Courses

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

​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.

Textul de pe ultima copertă

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.

Caracteristici

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