Quantum Groups: A Path to Current Algebra

Ross Street

ene 2007 · Australian Mathematical Society Lecture Series Libro 19 · Cambridge University Press

Acerca de este libro electrónico

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.

Acerca del autor

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.