James E. Humphreys
2000 Mathematics Subject Classification. Primary 17B37.
ABSTRACT. This book is an introduction to the theory of quantum groups. Its main objects are
the quantized enveloping algebras introduced independently by Drinfeld and Jimbo. We study
their finite dimensional representations, their centers, and their bases. In particular, we look at
the crystal (or canonical) bases discovered independently by Lusztig and Kashiwara.
We first look at the quantum analogue of the Lie algebra SI2, and then at the quantum analogue
of arbitrary finite dimensional complex Lie algebras. The book is directed to anyone who wants to
learn the subject and has been introduced to the theory of finite dimensional complex Lie algebras.
Library of Congress Cataloging-in-Publication Data
Jantzen, Jens Carsten.
Lectures on quantum groups / Jens Carsten Jantzen.
p. cm. — (Graduate studies in mathematics, ISSN 1065-7339; v. 6)
Includes bibliographical references and index.
ISBN 0-8218-0478-2 (alk. paper)
1. Quantum groups. 2. Mathematical physics. I. Title. II. Series.
QC20.7.G70J36 1995 95-25393
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© 1996 by the American Mathematical Society. All rights reserved.
Reprinted by the American Mathematical Society, 1997, 2009.
Printed in the United States of America.
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