Quartic trace identity for exceptional Lie algebras
Journal Article
·
· J. Math. Phys. (N.Y.); (United States)
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
Similar Records
Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras
On Exceptional Superconformal Algebras
Adjoint operators in Lie algebras and the classification of simple flexible Lie-admissible algebras
Journal Article
·
Mon Jul 15 00:00:00 EDT 2013
· Journal of Mathematical Physics
·
OSTI ID:22218262
On Exceptional Superconformal Algebras
Journal Article
·
Thu Jun 17 00:00:00 EDT 2010
· AIP Conference Proceedings
·
OSTI ID:21366959
Adjoint operators in Lie algebras and the classification of simple flexible Lie-admissible algebras
Journal Article
·
Tue Mar 31 23:00:00 EST 1981
· Trans. Am. Math. Soc.; (United States)
·
OSTI ID:6319338