E-Book Overview
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.The differences between complex algebraic groups and complex Lie groups are sometimes subtle and it can be difficult to know which aspects of algebraic group theory apply and which must be modified. The Structure of Complex Lie Groups helps clarify those distinctions. Clearly written and well organized, this unique work presents material not found in other books on Lie groups and serves as an outstanding complement to them.
E-Book Content
Dong Hoon Lee Department of Mathematics Case Western Reserve University
The structure of complex Lie groups
CHAPMAN & HALL/CRC Boca Raton London New York Washington, D.C.
Library of Congress Cataloging-in-Publication Data Lee, Dong Hoon, 1938The structure of complex Lie groups / Dong Hoon Lee. p. cm. — (Research notes in mathematics) Includes bibliographical references and index. ISBN 1-58488-261-1 (alk. paper) 1. Lie groups. I. Title. II. Chapman & Hall/CRC research notes in mathematics series. QA38