An introduction to Hopf algebras
The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging connections to fields from theoretical physics to computer science. This text is unique in...
Gardado en:
| Autor Principal: | |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
New York, NY :
Springer New York
2011.
Cham : Springer Nature |
| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to Hopf algebras, Robert G. Underwood, New York, N.Y., Springer Science+Business Media, LLC, 2011, 1 vol. (XIV-273 p.), 978-0-387-72765-3 • Visions and strategies in European integration, a North European perspective, Lars Lundqvist, Lars Olof Persson, eds, Berlin, Springer-Verlag, 1993, 1 vol. (ix-290 p.), 3-540-56615-5 • An Introduction to Hopf Algebras, Texte imprimé, 9781489997845 |
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| 100 | 1 | |a Underwood, Robert G. | |
| 245 | 1 | 0 | |a An introduction to Hopf algebras |c Robert G. Underwood. |
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c 2011. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a Preface -- Some Notation -- 1. The Spectrum of a Ring.-2. The Zariski Topology on the Spectrum.-3. Representable Group Functors.-4. Hopf Algebras. -5. Larson Orders.-6. Formal Group Hopf Orders.-7. Hopf Orders in KC_p.-8. Hopf Orders in KC_{p^2}.-9. Hopf Orders in KC_{p^3}.-10. Hopf Orders and Galois Module Theory.-11. The Class Group of a Hopf Order.-12. Open Questions and Research Problems.-Bibliography.-Index. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging connections to fields from theoretical physics to computer science. This text is unique in making this engaging subject accessible to advanced graduate and beginning graduate students and focuses on applications of Hopf algebras to algebraic number theory and Galois module theory, providing a smooth transition from modern algebra to Hopf algebras. After providing an introduction to the spectrum of a ring and the Zariski topology, the text treats presheaves, sheaves, and representable group functors. In this way the student transitions smoothly from basic algebraic geometry to Hopf algebras. The importance of Hopf orders is underscored with applications to algebraic number theory, Galois module theory and the theory of formal groups. By the end of the book, readers will be familiar with established results in the field and ready to pose research questions of their own. An exercise set is included in each of twelve chapters with questions ranging in difficulty. Open problems and research questions are presented in the last chapter. Prerequisites include an understanding of the material on groups, rings, and fields normally covered in a basic course in modern algebra. | ||
| 650 | |a Groupes, Théorie des | ||
| 650 | |a Anneaux commutatifs | ||
| 760 | 0 | |t Mathematics and Statistics | |
| 776 | 0 | |0 16649691X |t An introduction to Hopf algebras |f Robert G. Underwood |c New York, N.Y. |n Springer Science+Business Media, LLC |d 2011 |p 1 vol. (XIV-273 p.) |z 978-0-387-72765-3 | |
| 776 | 0 | |0 016950399 |t Visions and strategies in European integration |o a North European perspective |f Lars Lundqvist, Lars Olof Persson, eds |c Berlin |n Springer-Verlag |d 1993 |p 1 vol. (ix-290 p.) |z 3-540-56615-5 | |
| 776 | 0 | |t An Introduction to Hopf Algebras |b Texte imprimé |z 9781489997845 | |
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| 856 | 4 | |5 452349901:750611782 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.1007/978-0-387-72766-0 |z Accès Université d'Orléans | |
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