Classical Lie Groups

  • Joachim HilgertEmail author
  • Karl-Hermann Neeb
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, we apply the general theory to classical matrix groups such as \(\mathop {\mathrm {GL}}\nolimits _{n}({\mathbb{C}}), \mathop {\rm SL}\nolimits _{n}({\mathbb{C}}), \mathop {\rm SO}\nolimits _{n}({\mathbb{C}}), \mathop {\rm Sp}\nolimits _{2n}({\mathbb{C}})\), and some of their real forms to provide explicit structural and topological information. We will start with compact real forms, i.e., \(\mathop {\rm U{}}\nolimits _{n}({\mathbb{K}})\) and \(\mathop {\rm SU}\nolimits _{n}({\mathbb{K}})\), where \({\mathbb{K}}\) is ℝ, ℂ, or ℍ, since many results can be reduced to compact groups.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of PaderbornPaderbornGermany
  2. 2.Department of MathematicsFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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