Mathematical Notes

, Volume 77, Issue 3–4, pp 414–423 | Cite as

On graphs and Lie rings

  • Yu. S. Semenov


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.

Key words

graph subtree Lie ring adjoint Lie ring nilpotent finite-dimensional Lie algebra free ℤ-module contravariant functor 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yu. S. Semenov
    • 1
  1. 1.Moscow State University of Railway EngineeringMoscow

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