The Structure of Complex Lie Groups (Chapman & Hall/CRC Research Notes in Mathematics Series) 1st Edition by Dong Hoon Lee (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am quite familiar with Lie Algebras and Lie Groups, especially in the context of their applications to physics. I bought this book in the hope that I can learn more about the Complex extensions of Lie groups. Unfortunately, after trying to read the book for over a year, I still did not manage to get past the first 60 pages. The approach is very rigorous, but it is equally dry, and terse. The author makes no attempt to motivate the direction of exploration, and he offers no intuitive understanding of the topics. Applications and examples to demonstrate the theorems and concepts do not exist at all.If you are at the forefront of mathematical research on Lie groups, you may find this book very useful, even interesting. For the rest of us, it is practically useless. Physicists should stay away from this book, unless they possess an exceptional background in the topics covered.

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