001052370 001__ 1052370
001052370 005__ 20260123203315.0
001052370 0247_ $$2doi$$a10.48550/ARXIV.2601.16161
001052370 037__ $$aFZJ-2026-00964
001052370 088__ $$2arXiv$$a2601.16161
001052370 1001_ $$0P:(DE-Juel1)200494$$aHeib, Tim$$b0$$eCorresponding author$$ufzj
001052370 245__ $$aOn the structural properties of Lie algebras via associated labeled directed graphs
001052370 260__ $$barXiv$$c2026
001052370 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1769169077_4035
001052370 3367_ $$2ORCID$$aWORKING_PAPER
001052370 3367_ $$028$$2EndNote$$aElectronic Article
001052370 3367_ $$2DRIVER$$apreprint
001052370 3367_ $$2BibTeX$$aARTICLE
001052370 3367_ $$2DataCite$$aOutput Types/Working Paper
001052370 520__ $$aWe present a method for associating labeled directed graphs to finite-dimensional Lie algebras, thereby enabling rapid identification of key structural algebraic features. To formalize this approach, we introduce the concept of graph-admissible Lie algebras and analyze properties of valid graphs given the antisymmetry property of the Lie bracket as well as the Jacobi identity. Based on these foundations, we develop graph-theoretic criteria for solvability, nilpotency, presence of ideals, simplicity, semisimplicity, and reductiveness of an algebra. Practical algorithms are provided for constructing such graphs and those associated with the lower central series and derived series via an iterative pruning procedure. This visual framework allows for an intuitive understanding of Lie algebraic structures that goes beyond purely visual advantages, since it enables a simpler and swifter grasping of the algebras of interest beyond computational-heavy approaches. Examples, which include the Schrödinger and Lorentz algebra, illustrate the applicability of these tools to physically relevant cases. We further explore applications in physics, where the method facilitates computation of similtude relations essential for determining quantum mechanical time evolution via the Lie algebraic factorization method. Extensions to graded Lie algebras and related conjectures are discussed. Our approach bridges algebraic and combinatorial perspectives, offering both theoretical insights and computational tools into this area of mathematical physics.
001052370 536__ $$0G:(DE-HGF)POF4-5221$$a5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522)$$cPOF4-522$$fPOF IV$$x0
001052370 536__ $$0G:(BMBF)13N15685$$aVerbundprojekt: German Quantum Computer based on Superconducting Qubits (GEQCOS) - Teilvorhaben: Charakterisierung, Kontrolle und Auslese (13N15685)$$c13N15685$$x1
001052370 588__ $$aDataset connected to DataCite
001052370 650_7 $$2Other$$aMathematical Physics (math-ph)
001052370 650_7 $$2Other$$aQuantum Physics (quant-ph)
001052370 650_7 $$2Other$$aFOS: Physical sciences
001052370 7001_ $$0P:(DE-Juel1)185963$$aBruschi, David Edward$$b1$$ufzj
001052370 773__ $$a10.48550/ARXIV.2601.16161
001052370 909CO $$ooai:juser.fz-juelich.de:1052370$$pVDB
001052370 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)200494$$aForschungszentrum Jülich$$b0$$kFZJ
001052370 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)185963$$aForschungszentrum Jülich$$b1$$kFZJ
001052370 9131_ $$0G:(DE-HGF)POF4-522$$1G:(DE-HGF)POF4-520$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5221$$aDE-HGF$$bKey Technologies$$lNatural, Artificial and Cognitive Information Processing$$vQuantum Computing$$x0
001052370 9141_ $$y2026
001052370 920__ $$lyes
001052370 9201_ $$0I:(DE-Juel1)PGI-12-20200716$$kPGI-12$$lQuantum Computing Analytics$$x0
001052370 980__ $$apreprint
001052370 980__ $$aVDB
001052370 980__ $$aI:(DE-Juel1)PGI-12-20200716
001052370 980__ $$aUNRESTRICTED