國立虎尾科技大學 |

Quantum Groups and Noncommutative Geometry

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Quantum Groups and Noncommutative Geometry/ by Yuri I. Manin.
Author:	Manin, Yuri I.
Description:	VIII, 125 p. 83 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Associative rings. -
Online resource:	https://doi.org/10.1007/978-3-319-97987-8
ISBN:	9783319979878

Quantum Groups and Noncommutative Geometry
Manin, Yuri I.

Quantum Groups and Noncommutative Geometry[electronic resource] /by Yuri I. Manin. - 2nd ed. 2018. - VIII, 125 p. 83 illus., 1 illus. in color.online resource. - 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

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

893564
Associative rings.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Quantum Groups and Noncommutative Geometry
LDR:02964nam a22004095i 4500 001 988750
003 DE-He213
005 20200629134631.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319979878 $9 978-3-319-97987-8
024 7 $a 10.1007/978-3-319-97987-8 $2 doi
035 $a 978-3-319-97987-8
050 4 $a QA251.5
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.46 $2 23
100 1 $a Manin, Yuri I. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1205137
245 1 0 $a Quantum Groups and Noncommutative Geometry $h [electronic resource] / $c by Yuri I. Manin.
250 $a 2nd ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a VIII, 125 p. 83 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Associative rings. $3 893564
650 0 $a Rings (Algebra). $3 685051
650 0 $a Group theory. $3 527791
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Homological algebra. $3 1255326
650 1 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Category Theory, Homological Algebra. $3 678397
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319979861
776 0 8 $i Printed edition: $z 9783319979885
776 0 8 $i Printed edition: $z 9783030074326
830 0 $a CRM Short Courses, $x 2522-5200 $3 1280861
856 4 0 $u https://doi.org/10.1007/978-3-319-97987-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)