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    • Keywords


      Infinite dimensional Lie algebras; split Lie algebras; roots.

    • Abstract


      We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such algebras 𝐿 is of the form $L=\mathcal{U}+\sum_j I_j$ with $\mathcal{U}$ a subspace of the abelian Lie algebra 𝐻 and any $I_j$ a well described ideal of 𝐿, satisfying $[I_j,I_k]=0$ if $j\neq k$. Under certain conditions, the simplicity of 𝐿 is characterized and it is shown that 𝐿 is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected.

    • Author Affiliations


      Antonio J Calderón Martín1

      1. Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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