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### Published volumes

##### 1936-1944
$T^*$-extensions and abelian extensions of hom-Lie color algebras
Volume 59, no. 1 (2018), pp. 123–142

DOI: https://doi.org/10.33044/revuma.v59n1a06

### Abstract

We study hom-Nijenhuis operators, $T^ \ast$-extensions and abelian extensions of hom-Lie color algebras. We show that the infinitesimal deformation generated by a hom-Nijenhuis operator is trivial. Many properties of a hom-Lie color algebra can be lifted to its $T^ \ast$-extensions such as nilpotency, solvability and decomposition. It is proved that every finite-dimensional nilpotent quadratic hom-Lie color algebra over an algebraically closed field of characteristic not 2 is isometric to a $T^ \ast$-extension of a nilpotent Lie color algebra. Moreover, we introduce abelian extensions of hom-Lie color algebras and show that there is a representation and a 2-cocycle, associated to any abelian extension.