On (α,β,γ)-derivations of Lie algebras and corresponding invariant functions

2007/11/14 by Petr Novotný, Jiří Hrivnák · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math-ph #math.MP #msc:17B05 #msc:17B40

paper · pdf · doi:10.1016/j.geomphys.2007.10.005

published as Journal of Geometry and Physics 58 (2008) 208-217 · 12 pages

openalex publication_date 2007/11/14 · arxiv created 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• A class of solvable Lie algebras and their Casimir invariants
• Generalized Derivations of Lie Algebras

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• Twisted cocycles of lie algebras and corresponding invariant functions