Del 19 i serien Australian Mathematical Society Lecture Series

Quantum Groups

A Path to Current Algebra

Häftad, Engelska, 2007

959 kr

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Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.

Produktinformation

Utgivningsdatum2007-01-18
Mått152 x 229 x 9 mm
Vikt240 g
FormatHäftad
SpråkEngelska
SerieAustralian Mathematical Society Lecture Series
Antal sidor160
FörlagCambridge University Press
ISBN9780521695244

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Matematikens grunder inom Naturvetenskap och teknik

Introduction; 1. Revision of basic structures; 2. Duality between geometry and algebra; 3. The quantum general linear group; 4. Modules and tensor products; 5. Cauchy modules; 6. Algebras; 7. Coalgebras and bialgebras; 8. Dual coalgebras of algebras; 9. Hopf algebras; 10. Representations of quantum groups; 11. Tensor categories; 12. Internal homs and duals; 13. Tensor functors and Yang-Baxter operators; 14. A tortile Yang-Baxter operator for each finite-dimensional vector space; 15. Monoids in tensor categories; 16. Tannaka duality; 17. Adjoining an antipode to a bialgebra; 18. The quantum general linear group again; 19. Solutions to exercises; References; Index.