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This is a graduate-level text that systematically develops the foundations of the subject. Quantum groups (i.e. Hopf algebras) are treated as mathematical objects in their own right; basic properties and theorems are proven in detail from this standpoint, including the results underlying key applications. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. The explicit proofs and a great many worked examples and exercises will allow readers to quickly pick up the techniques needed for working in this exciting new field.
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"...this is a remarkable book, written in a rigorous style (all necessary statements are proved explicitly) by an acknowledged leader in the field." Dmitrii I. Gurevich, Mathematical Reviews
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- PublisherCambridge University Press
- Publication date2008
- ISBN 10 0521648688
- ISBN 13 9780521648684
- BindingPaperback
- Number of pages664
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