Invariant bilinear forms on real irreducible representations of real semisimple lie algebras * : Communications in Algebra: Vol 28, No 9

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Abstract

In this note, we give a necessary and sufficient condition for a real irreducible representation of a real simple Lie algebra to admit an invariant bilinear form. We also determine when the invariant bilinear form is symmetric or skew-symmetric.

^*This work is supported by the National Natural Science Foundation of China (No. 19901015) and the National Postdoctoral Foundation of China

Notes

^*This work is supported by the National Natural Science Foundation of China (No. 19901015) and the National Postdoctoral Foundation of China

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Invariant bilinear forms on real irreducible representations of real semisimple lie algebrasFootnote^*
^*This work is supported by the National Natural Science Foundation of China (No. 19901015) and the National Postdoctoral Foundation of China

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Invariant bilinear forms on real irreducible representations of real semisimple lie algebrasFootnote**This work is supported by the National Natural Science Foundation of China (No. 19901015) and the National Postdoctoral Foundation of China

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Invariant bilinear forms on real irreducible representations of real semisimple lie algebrasFootnote^*
^*This work is supported by the National Natural Science Foundation of China (No. 19901015) and the National Postdoctoral Foundation of China