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Complex Semisimple Lie Groups

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Part of the Springer Series in Soviet Mathematics book series (SSSOV)

Abstract

This chapter deals with the most explored section of the theory of Lie groups and Lie algebras. Its main result is the complete classification of connected complex semisimple Lie groups and their irreducible linear representations. This classification is based on the theory of root systems, which because of its numerous applications deserves a special treatment. The theory is axiomatically developed in §2. During the whole chapter (except 1.1°–1.3°) the ground field is ℂ. All the vector spaces and Lie algebras considered are finite-dimensional.

Keywords

  • Algebraic Group
  • Simple Root
  • Maximal Torus
  • Dynkin Diagram
  • Borel Subgroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-74334-4_4
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© 1990 Springer-Verlag Berlin Heidelberg

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Onishchik, A.L., Vinberg, E.B. (1990). Complex Semisimple Lie Groups. In: Lie Groups and Algebraic Groups. Springer Series in Soviet Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74334-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-74334-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74336-8

  • Online ISBN: 978-3-642-74334-4

  • eBook Packages: Springer Book Archive