Real forms of a Lie algebra

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Pythagoras0 (토론 | 기여)님의 2020년 12월 27일 (일) 03:16 판 (→‎메타데이터: 새 문단)
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introduction

  • a complex Lie algbera L can be regarded as a real Lie algebra \(L^{R}\)
  • if \(L^{R}=L_0\oplus i L_0\) for some real subalgebra \(L_0\)
  • \(L_0\) is called a real from of \(L\)
  • split real forms
  • compact real forms


compact real forms

  • of all the real forms of a given simple complex Lie algebra, there is precisely one which is the real Lie algebra of a compact Lie group
  • a real Lie algebra which is the Lie algebra of some compact group is called compact

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