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

Abstract

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.

arXiv comment12 pages

References in corpus (4)

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• A class of solvable Lie algebras and their Casimir Invariants
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Cited by in corpus (8)

• (n+1)-Ary derivations os semisimple Filippov algebras
• A generalization on derivations of Lie algebras
• Twisted cocycles of Lie algebras and corresponding invariant functions
• Graded contractions of the Gell-Mann graded sl(3,C)
• Lie-orthogonal operators
• Generalized conformal derivations of Lie conformal algebras
• Generalized derivations and Hom-Lie algebra structures on ${\mathfrak{sl}}_2$
• (Bi)Hom-Leibniz algebras