Springer Monographs in Mathematics

Complex Semisimple Lie Algebras

Authors: Serre, Jean-Pierre

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About this book

These short notes, already well-known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers, including classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and linear representations. The last chapter discusses the connection between Lie algebras, complex groups and compact groups; it is intended to guide the reader towards further study.

Reviews

From the reviews of the French edition:

"...the book is intended for those who have an acquaintance with the basic parts of the theory, namely, with those general theorems on Lie algebras which do not depend on the notion of Cartan subalgebra. The author begins with a summary of these general theorems and then discusses in detail the structure and representation theory of complex semisimple Lie algebras. One recognizes here a skillful ordering of the material, many simplifications of classical arguments and a new theorem describing fundamental relations between canonical generators of semisimple Lie algebras. The classical theory being thus introduced in such modern form, the reader can quickly reach the essence of the theory through the present book." (Mathematical Reviews)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-642-56884-8
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-540-67827-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $59.99
price for USA in USD
  • ISBN 978-3-642-63222-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Complex Semisimple Lie Algebras
Authors
Translated by
Jones, G.A.
Series Title
Springer Monographs in Mathematics
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-56884-8
DOI
10.1007/978-3-642-56884-8
Hardcover ISBN
978-3-540-67827-4
Softcover ISBN
978-3-642-63222-8
Series ISSN
1439-7382
Edition Number
1
Number of Pages
IX, 75
Additional Information
Original French edition published by Benjamin, New York, 1966. Former English edition published as a monograph
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