Quantum Groups

A Path to Current Algebra

By: Ross Street

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eText | 18 January 2007 | Edition Number 1

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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 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.