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[null,"1.","Record Nr.",null,"UNINA9910300133303321"]
[null,null,"Autore",null,"Manin Yuri I"]
[null,null,"Titolo",null,"Quantum Groups and Noncommutative Geometry / / by Yuri I. Manin"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018"]
[null,null,"ISBN",null,"3-319-97987-6"]
[null,null,"Edizione",null,"[2nd ed. 2018.]"]
[null,null,"Descrizione fisica",null,"1 online resource (VII, 125 p. 18 illus.)"]
[null,null,"Collana",null,"CRM Short Courses, , 2522-5200"]
[null,null,"Disciplina",null,"516.35"]
[null,null,"Soggetti",null,"Associative rings"]
[{"$nulls":4},"Rings (Algebra)"]
[{"$nulls":4},"Group theory"]
[{"$nulls":4},"Categories (Mathematics)"]
[{"$nulls":4},"Algebra, Homological"]
[{"$nulls":4},"Associative Rings and Algebras"]
[{"$nulls":4},"Group Theory and Generalizations"]
[{"$nulls":4},"Category Theory, Homological Algebra"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"1. The Quantum Group GL(2) -- 2. Bialgebras and Hopf Algebras -- 3. Quadratic Algebras as Quantum Linear Spaces -- 4. Quantum Matrix Spaces. I. Categorical Viewpoint -- 5. Quantum Matrix Spaces. II. Coordinate Approach -- 6. Adding Missing Relations -- 7. From Semigroups to Groups -- 8. Frobenius Algebras and the Quantum Determinant -- 9. Koszul Complexes and the Growth Rate of Quadratic Algebras -- 10. Hopf *-Algebras and Compact Matrix Pseudogroups -- 11. Yang-Baxter Equations -- 12. Algebras in Tensor Categories and Yang-Baxter Functors -- 13. Some Open Problems -- 14. The Tannaka–Krein Formalism and (Re)Presentations of Universal Quantum Groups -- Bibliography -- Index."]
[null,null,null,"Sommario/riassunto","This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new "]
[{"$nulls":4},"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."]