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024 7 $a10.1007/978-3-319-97987-8
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100   $a20181011d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aQuantum Groups and Noncommutative Geometry /$fby Yuri I. Manin
205   $a2nd ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (VII, 125 p. 18 illus.) 
225 1 $aCRM Short Courses,$x2522-5200
311   $a3-319-97986-8 
327   $a1. 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.
330   $aThis textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka?Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.
410  0$aCRM Short Courses,$x2522-5200
606   $aAssociative rings
606   $aRings (Algebra)
606   $aGroup theory
606   $aCategories (Mathematics)
606   $aAlgebra, Homological
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
615  0$aAssociative rings.
615  0$aRings (Algebra)
615  0$aGroup theory.
615  0$aCategories (Mathematics)
615  0$aAlgebra, Homological.
615 14$aAssociative Rings and Algebras.
615 24$aGroup Theory and Generalizations.
615 24$aCategory Theory, Homological Algebra.
676   $a516.35
700   $aManin$b Yuri I$4aut$4http://id.loc.gov/vocabulary/relators/aut$049026
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300133303321
996   $aQuantum Groups and Noncommutative Geometry$91563731
997   $aUNINA