On split regular Hom-Lie color algebras

Yan Cao ¹   ; Liangyun Chen ²

¹ School 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
² School of Mathematics and Statistics Northeast Normal University 130024 Changchun, China

Colloquium Mathematicum, Tome 146 (2017) no. 1, pp. 143-155

Résumé

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.

Détail

DOI : 10.4064/cm6769-12-2015

Keywords: introduce class split regular hom lie color algebras natural generalization split lie color algebras developing techniques connections roots kind algebras every split regular hom lie color algebra form sum varlambda sim subspace abelian graded subalgebra well described ideal satisfying under certain conditions being maximal length simplicity algebra characterized