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On a quaternification of complex Lie algebras

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 نشر من قبل Toshiaki Kori
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Kori Tosiaki




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We give a definition of quaternion Lie algebra and of the quaternification of a complex Lie algebra. By our definition gl(n,H), sl(n,H), so*(2n) ans sp(n) are quaternifications of gl(n,C), sl(n,C), so(n,C) and u(n) respectively. Then we shall prove that a simple Lie algebra admits the quaternification. For the proof we follow the well known argument due to Harich-Chandra, Chevalley and Serre to construct the simple Lie algebra from its corresponding root system. The root space decomposition of this quaternion Lie algebra will be given. Each root sapce of a fundamental root is complex 2-dimensional.



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