An Introduction to Hopf Algebras [recurso electrónico] / by Robert G. Underwood.
Tipo de material: TextoEditor: New York, NY : Springer New York : Imprint: Springer, 2011Descripción: XIV, 273 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9780387727660Tema(s): Mathematics | Algebra | Group theory | Mathematics | Algebra | Commutative Rings and Algebras | Group Theory and GeneralizationsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512 Clasificación LoC:QA150-272Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA150 -272 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 370225-2001 |
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QA1 -939 Mathematical Analysis II | QA1 -939 Algebra lineare ed equazioni differenziali ordinarie | QA1 -939 Matematica e cultura 2011 | QA150 -272 An Introduction to Hopf Algebras | QA150 -272 The Colorado Mathematical Olympiad and Further Explorations | QA150 -272 Representations of SL2(Fq) | QA150 -272 Representation Theory of the Virasoro Algebra |
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.
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.
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