On (alpha,beta,gamma)-derivations of Lie algebras and corresponding invariant functions

Details On (alpha,beta,gamma)-derivations of Lie algebras and corresponding invariant functions On (alpha,beta,gamma)-derivations of Lie algebras and corresponding invariant functions

2008-03-18

arxiv.org/abs/0803.2682v1

Journal of Geometry and Physics 58 (2008) 208-217

Physics

Mathematical Physics

12 pages

Scientific paper

10.1016/j.geomphys.2007.10.005

We consider finite-dimensional complex Lie algebras. We generalize the concept of Lie derivations via certain complex parameters and obtain various Lie and Jordan operator algebras as well as two one-parametric sets of linear operators. Using these parametric sets, we introduce complex functions with fundamental property - invariance under Lie isomorphisms. One of these basis-independent functions represents a complete set of invariant(s) for three-dimensional Lie algebras. We present also its application on physically motivated examples in dimension eight.

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