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On split regular Hom-Lie color algebras

Volume 146 / 2017

Yan Cao, Liangyun Chen Colloquium Mathematicum 146 (2017), 143-155 MSC: 17B75, 17A60, 17B22, 17B65. DOI: 10.4064/cm6769-12-2015 Published online: 23 September 2016

Abstract

We introduce the class of split regular Hom-Lie color algebras as a natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that every split regular Hom-Lie color algebra $L$ is of the form $L = U + \sum _{[j] \in \varLambda /\!\sim }I_{[j]}$ with $U$ a subspace of an abelian graded subalgebra $H$ and any $I_{[j]}$ a well-described ideal of $L$, satisfying $[I_{[j]}, I_{[k]}] = 0$ if $[j]\not =[k]$. Under certain conditions, in the case of $L$ being of maximal length, the simplicity of the algebra is characterized.

Authors

  • Yan CaoSchool of Mathematics and Statistics
    Northeast Normal University
    130024 Changchun, China
    and
    Department of Basic Education
    Harbin University of Science and Technology
    Rongcheng Campus
    264300 Rongcheng, China
    e-mail
  • Liangyun ChenSchool of Mathematics and Statistics
    Northeast Normal University
    130024 Changchun, China
    e-mail

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