# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Artykuły Online First

## Split regular Hom-Leibniz color 3-algebras

Colloquium Mathematicum MSC: Primary 17A60, 17A32, 17A40. DOI: 10.4064/cm7671-9-2018 Opublikowany online: 24 May 2019

#### Streszczenie

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.

#### Autorzy

• Ivan KaygorodovUniversidade Federal do ABC, CMCC
Av. dos Estado, 5001 - Bangú
Santo André - SP, 09210-580, Brazil
e-mail