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Quartic trace identity for exceptional Lie algebras

Journal Article · · J. Math. Phys. (N.Y.); (United States)
DOI:https://doi.org/10.1063/1.524127· OSTI ID:6198137
Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation )lambda) of the Lie algebra. Then, for all exceptional Lie algebras as well as A/sub 1/ and A/sub 2/, we can prove the validity of a quartic trace identity Tr(X/sup 4/) =K (lambda)(Tr(X/sup 2/))/sup 2/, where the constant K (lambda) depends only upon the irreducible representation )lambda), and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed.
Research Organization:
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627
OSTI ID:
6198137
Journal Information:
J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 20:4; ISSN JMAPA
Country of Publication:
United States
Language:
English

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