Home > Publications database > On the structural properties of Lie algebras via associated labeled directed graphs > print

001     1052370
005     20260123203315.0
024 7 _ |a 10.48550/ARXIV.2601.16161
|2 doi
037 _ _ |a FZJ-2026-00964
088 _ _ |a 2601.16161
|2 arXiv
100 1 _ |a Heib, Tim
|0 P:(DE-Juel1)200494
|b 0
|e Corresponding author
|u fzj
245 _ _ |a On the structural properties of Lie algebras via associated labeled directed graphs
260 _ _ |c 2026
|b arXiv
336 7 _ |a Preprint
|b preprint
|m preprint
|0 PUB:(DE-HGF)25
|s 1769169077_4035
|2 PUB:(DE-HGF)
336 7 _ |a WORKING_PAPER
|2 ORCID
336 7 _ |a Electronic Article
|0 28
|2 EndNote
336 7 _ |a preprint
|2 DRIVER
336 7 _ |a ARTICLE
|2 BibTeX
336 7 _ |a Output Types/Working Paper
|2 DataCite
520 _ _ |a We 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.
536 _ _ |a 5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522)
|0 G:(DE-HGF)POF4-5221
|c POF4-522
|f POF IV
|x 0
536 _ _ |a Verbundprojekt: German Quantum Computer based on Superconducting Qubits (GEQCOS) - Teilvorhaben: Charakterisierung, Kontrolle und Auslese (13N15685)
|0 G:(BMBF)13N15685
|c 13N15685
|x 1
588 _ _ |a Dataset connected to DataCite
650 _ 7 |a Mathematical Physics (math-ph)
|2 Other
650 _ 7 |a Quantum Physics (quant-ph)
|2 Other
650 _ 7 |a FOS: Physical sciences
|2 Other
700 1 _ |a Bruschi, David Edward
|0 P:(DE-Juel1)185963
|b 1
|u fzj
773 _ _ |a 10.48550/ARXIV.2601.16161
909 C O |o oai:juser.fz-juelich.de:1052370
|p VDB
910 1 _ |a Forschungszentrum Jülich
|0 I:(DE-588b)5008462-8
|k FZJ
|b 0
|6 P:(DE-Juel1)200494
910 1 _ |a Forschungszentrum Jülich
|0 I:(DE-588b)5008462-8
|k FZJ
|b 1
|6 P:(DE-Juel1)185963
913 1 _ |a DE-HGF
|b Key Technologies
|l Natural, Artificial and Cognitive Information Processing
|1 G:(DE-HGF)POF4-520
|0 G:(DE-HGF)POF4-522
|3 G:(DE-HGF)POF4
|2 G:(DE-HGF)POF4-500
|4 G:(DE-HGF)POF
|v Quantum Computing
|9 G:(DE-HGF)POF4-5221
|x 0
914 1 _ |y 2026
920 _ _ |l yes
920 1 _ |0 I:(DE-Juel1)PGI-12-20200716
|k PGI-12
|l Quantum Computing Analytics
|x 0
980 _ _ |a preprint
980 _ _ |a VDB
980 _ _ |a I:(DE-Juel1)PGI-12-20200716
980 _ _ |a UNRESTRICTED

LibraryCollectionCLSMajorCLSMinorLanguageAuthor
Marc 21