Abstract:
From a finite oriented graph $\Gamma$, finite-dimensional graded nilpotent Lie rings $\mathfrak l(\Gamma)$ and $\mathfrak g(\Gamma)$ are naturally constructed; these rings are related to subtrees and connected subgraphs of $\Gamma$, respectively. Diverse versions of these constructions are also suggested. Moreover, an embedding of Lie rings of the form $\mathfrak l(\Gamma)$ in the adjoint Lie rings of finite-dimensional associative rings (also determined by the graph $\Gamma$) is indicated.
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