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Quantum Groups : A Path to Current Algebra, PDF eBook

Quantum Groups : A Path to Current Algebra PDF

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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.

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