Quantum Groups
A Path to Current Algebra
CAD$90.95 (P)
Part of Australian Mathematical Society Lecture Series
- Author: Ross Street, Macquarie University, Sydney
- Date Published: January 2007
- availability: Available
- format: Paperback
- isbn: 9780521695244
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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.
Read more- Essential for any graduate student or researcher whose research involves quantum groups
- Containing the latest algebraic concepts and techniques, this book updates the meaning of 'modern algebra'
- Includes over 60 worked examples and exercises
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"The book is very well written [and] it is quite concise."
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×Product details
- Date Published: January 2007
- format: Paperback
- isbn: 9780521695244
- length: 160 pages
- dimensions: 229 x 152 x 9 mm
- weight: 0.24kg
- contains: 26 b/w illus. 25 exercises
- availability: Available
Table of Contents
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.
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