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Split regular Hom-Leibniz color 3-algebras

Volume 157 / 2019

Ivan Kaygorodov, Yury Popov Colloquium Mathematicum 157 (2019), 251-277 MSC: Primary 17A60, 17A32, 17A40. DOI: 10.4064/cm7671-9-2018 Published online: 24 May 2019


We introduce and describe the class of split regular Hom-Leibniz color $3$-algebras as the natural extension of the class of split Lie algebras and superalgebras.

More precisely, we show that any such split regular Hom-Leibniz color $3$-algebra $T$ is of the form $T=\mathcal {U} +\sum _{j}I_{j}$ with $\mathcal {U}$ a subspace of the $0$-root space ${T}_0$, and $I_{j}$ an ideal of $T$ such that for $j\not =k$, \[ [{ T},I_j,I_k]+[I_j,{ T},I_k]+[I_j,I_k,T]=0. \] Moreover, if $T$ is of maximal length, we characterize the simplicity of $T$ in terms of a connectivity property in its set of non-zero roots.


  • Ivan KaygorodovUniversidade Federal do ABC, CMCC
    Av. dos Estado, 5001 - Bangú
    Santo André - SP, 09210-580, Brazil
  • Yury PopovUniversidade Estadual de Campinas, IMECC
    Cidade Universitária
    Campinas - SP, 13083-859, Brazil

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