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.
Buy Quantum Groups book by Ross Street from Australia's Online Independent Bookstore, Boomerang Books.
(228mm x 152mm x 9mm)
Cambridge University Press
Publisher: Cambridge University Press
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Author Biography - Ross Street
Ross Street is a Professor of Mathematics and Director of the Centre of Australian Category Theory at Macquarie University. He is also a Fellow of the Australian Academy of Science.