Quartic trace identity for exceptional Lie algebras
- 1 April 1979
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 20 (4) , 586-593
- https://doi.org/10.1063/1.524127
Abstract
Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation {λ} of the Lie algebra. Then, for all exceptional Lie algebras as well as A1 and A2, we can prove the validity of a quartic trace identity Tr(X4) =K (λ)[Tr(X2)]2, where the constant K (λ) depends only upon the irreducible representation {λ}, and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed.Keywords
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