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Quantum groups : a path to current algebra

Author: Ross Street
Publisher: New York : Cambridge University Press, 2007.
Series: Australian Mathematical Society lecture series, 19.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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 who is at ease with at least one such structure and keen to learn the latest algebraic concepts and techniques." "A  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ross Street
ISBN: 0521695244 9780521695244
OCLC Number: 78576805
Description: xviii, 141 pages : illustrations ; 23 cm.
Contents: 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 horns 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.
Series Title: Australian Mathematical Society lecture series, 19.
Responsibility: Ross Street.
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Quantum Groups: A Path to Current Algebra presents algebraic concepts and techniques.  Read more...

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"The book is very well written [and] it is quite concise." E.J. Taft, Mathematical Reviews

 
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    schema:reviewBody ""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 who is 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."--BOOK JACKET." ;
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