Quantum Groups

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Springer New York, Dec 1, 1994 - Mathematics - 534 pages
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{( Eh bien, Monsieur, que pensez-vous des x et des y ? Je lui ai repondu : {( C'est bas de plafond. V. Hugo [Hug51] The term "quantum groups" was popularized by Drinfeld in his address to the International Congress of Mathematicians in Berkeley (1986). It stands for certain special Hopf algebras which are nontrivial deformations of the enveloping Hopf algebras of semisimple Lie algebras or of the algebras of regular functions on the corresponding algebraic groups. As was soon ob served, quantum groups have close connections with varied, a priori remote, areas of mathematics and physics. The aim of this book is to provide an introduction to the algebra behind the words "quantum groups" with emphasis on the fascinating and spec tacular connections with low-dimensional topology. Despite the complexity of the subject, we have tried to make this exposition accessible to a large audience. We assume a standard knowledge of linear algebra and some rudiments of topology (and of the theory of linear differential equations as far as Chapter XIX is concerned).

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Kassel's Quantum Groups is beautifully written, and includes all the necessary materials for a solid introduction to quantum groups. Perhaps one large advantage this book has over Jantzen's book (Lectures on Quantum Groups) is its treatment of Hopf algebras in the introductory sections, as well as the breadth of exercises at the end of each chapter. This makes the text especially useful for a introductory course on quantum groups (at the graduate level).
We used this book for a reading course on quantum groups. My only complaint would be that there are still some errors in the exercises, as well as in some of the main content. This could make working through the text on your own difficult at times, although I did not find this to be that big of a problem. Overall the text was a perfect fit.

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