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  • Cited by 39
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
2007
Online ISBN:
9780511618505
DOI:
https://doi.org/10.1017/CBO9780511618505
Subjects:
Mathematics (general), Mathematics, Physics and Astronomy, Logic, Categories and Sets, Theoretical Physics and Mathematical Physics
Series:
Australian Mathematical Society Lecture Series (19)
Information

Book 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 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.

Reviews

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

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