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Quantum groups and noncommutative ge...

Manin, Yuri I.

Quantum groups and noncommutative geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum groups and noncommutative geometryby Yuri I. Manin.
Author:	Manin, Yuri I.
Published:	Cham :Springer International Publishing :2018.
Description:	vii, 125 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Quantum groups.
Online resource:	https://doi.org/10.1007/978-3-319-97987-8
ISBN:	9783319979878$q(electronic bk.)

Quantum groups and noncommutative geometry
Manin, Yuri I.

Quantum groups and noncommutative geometry[electronic resource] /by Yuri I. Manin. - 2nd ed. - Cham :Springer International Publishing :2018. - vii, 125 p. :ill., digital ;24 cm. - CRM short courses,2522-5200. - CRM short courses..

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.

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.

ISBN: 9783319979878$q(electronic bk.)

Standard No.: 10.1007/978-3-319-97987-8doiSubjects--Topical Terms:

190852
Quantum groups.

LC Class. No.: QC20.7.G76 / M365 2018

Dewey Class. No.: 512.2

Quantum groups and noncommutative geometry
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245 1 0 $a Quantum groups and noncommutative geometry $h [electronic resource] / $c by Yuri I. Manin.
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260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a vii, 125 p. : $b ill., digital ; $c 24 cm.
490 1 $a CRM short courses, $x 2522-5200
505 0 $a 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.
520 $a 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.
650 0 $a Quantum groups. $3 190852
650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Noncommutative differential geometry. $3 266983
650 1 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Category Theory, Homological Algebra. $3 275954
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856 4 0 $u https://doi.org/10.1007/978-3-319-97987-8
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