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- W4300890254 abstract "Dani and Mainkar introduced a method for constructing a 2-step nilpotent Lie algebra $mathfrak{n}_G$ from a simple directed graph $G$ in 2005. There is a natural inner product on $mathfrak{n}_G$ arising from the construction. We study geometric properties of the associated simply connected 2-step nilpotent Lie group $N$ with Lie algebra $mathfrak{n}_G$. We classify singularity properties of the Lie algebra $mathfrak{n}_G$ in terms of the graph $G$. A comprehensive description is given of graphs $G$ which give rise to Heisenberg-like Lie algebras. Conditions are given on the graph $G$ and on a lattice $Gamma subseteq N$ for which the quotient $Gamma backslash N$, a compact nilmanifold, has a dense set of smoothly closed geodesics." @default.
- W4300890254 created "2022-10-04" @default.
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- W4300890254 date "2015-12-24" @default.
- W4300890254 modified "2023-09-25" @default.
- W4300890254 title "Graphs and Metric 2-step Nilpotent Lie Algebras" @default.
- W4300890254 doi "https://doi.org/10.48550/arxiv.1512.07944" @default.
- W4300890254 hasPublicationYear "2015" @default.
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