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Journal of Lie Theory 24 (2014), No. 2, 307--319
Copyright Heldermann Verlag 2014



An Explicit Rational Structure for Real Semisimple Lie Algebras

Holger Kammeyer
Mathematisches Institut, Universitšt Bonn, Endenicher Allee 60, 53115 Bonn, Germany
kammeyer@math.uni-bonn.de



We construct a convenient basis for all real semisimple Lie algebras by means of an adapted Chevalley basis of the complexification. It determines rational and in fact half-integer structure constants which we express only in terms of the root system and the involution that defines the real structure.

Keywords: Semisimple Lie algebra, rational basis, Chevalley basis.

MSC: 17B20

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