Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/46298
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- Title
- Quantum groups : a path to current algebra
- Related
- Australian Mathematical Society lecture series 19
- Publisher
- Cambridge : Cambridge University Press
- Date
- 2007
- FoR/RFCD Code(s)
-
230103 230104Rings and Algebras Category Theory, K Theory, Homological AlgebraRings and Algebras Category Theory, K Theory, Homological Algebra
010101 Algebra and Number Theory
010103 Category Theory, K Theory, Homological Algebra
- Author/Creator
- Street, Ross
- Description
- 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 the latest 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.
- Description
- 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 -- Index.
- Subject Keyword
- 230103 230104Rings and Algebras Category Theory, K Theory, Homological AlgebraRings and Algebras Category Theory, K Theory, Homological Algebra
- Subject Keyword
- 010101 Algebra and Number Theory
- Subject Keyword
- 010103 Category Theory, K Theory, Homological Algebra
- Subject Keyword
- Quantum groups
- Subject Keyword
- Algebra
- Resource Type
- book
- Organisation
- Macquarie University. Dept. of Mathematics
- Identifier
- http://hdl.handle.net/1959.14/46298
- Identifier
- ISBN:9780521695244
- Identifier
- mq-rm-2006000637
- Language
- eng
