On the structural properties of Lie algebras via associated labeled directed graphs
math-ph, math.MP, quant-ph
Submitted: 2026-01-22
Updated: 2026-10-20
Comments: We have significantly overhauled the manuscript. In particular, we have withdrawn Conjectures 80, 82, and 83 of the original version. The appendix has also been updated. 95 pages (66+29), 32 figures (24+8)
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Full classification of Pauli Lie algebras
- Lie algebras associated with labeled directed graphs
- Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
- The nilpotent graph of a finite0-dimensional Lie algebra
- Restricted graph Lie algebras in characteristic two
- A graph-theoretic approach to chaos and complexity in quantum systems
- Classification of solvable Lie algebras
- Finite-dimensional Lie algebras in bosonic quantum dynamics: The single-mode case
- Fibonacci numbers and the golden ratio
- Group gradings on classical Lie superalgebras
- Canonical forms for a class of pairs of commuting nilpotent matrices under simultaneous similarity
- Nilpotent Decomposition of Solvable Lie Algebras
- Formalizing a classification theorem for low-dimensional solvable Lie algebras in Lean
- Gaussian states in continuous variable quantum information
- Cohomology of perfect Lie algebras
- On the transitivity of Lie ideals and a characterization of perfect Lie algebras
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