2023/08/01 by Molina, Mauricio Godoy, Lagos, Diego
#05C20 #05C25 #17B30 #17B40 #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2308.00272
We present a construction of 2-step nilpotent Lie algebras using labeled directed simple graphs, which allows us to give a criterion to detect certain ideals and subalgebras by finding special subgraphs. We prove that if a label occurs only once, then reversing the orientation of that edge leads to an isomorphic Lie algebra. As a consequence, if every edge is labeled differently, the Lie algebra depends only on the underlying undirected graph. In addition, we construct the labeled directed graphs of all 2-step nilpotent Lie algebras of dimension ≤6 and we compute the algebra of strata preserving derivations of the Lie algebra associated with the complete bipartite graph Km,n with two different labelings.