Abstract
From a finite oriented graph Γ, finite-dimensional graded nilpotent Lie rings \(\mathfrak{l}\left( \Gamma \right)\)(Γ) and \(\mathfrak{g}\left( \Gamma \right)\)(Γ) are naturally constructed; these rings are related to subtrees and connected subgraphs of Γ, respectively. Diverse versions of these constructions are also suggested. Moreover, an embedding of Lie rings of the form \(\mathfrak{l}\left( \Gamma \right)\)(Γ) in the adjoint Lie rings of finite-dimensional associative rings (also determined by the graph Γ) is indicated.
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Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 449–459.
Original Russian Text Copyright © 2005 by Yu. S. Sernenov.
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Semenov, Y.S. On graphs and Lie rings. Math Notes 77, 414–423 (2005). https://doi.org/10.1007/s11006-005-0040-0
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DOI: https://doi.org/10.1007/s11006-005-0040-0