T ∗  -extensions and abelian extensions of hom-Lie color algebras.

Bing Sun ^[1] ; Liangyun Chen ; Yan Liu
1. [1] Northeast Normal University
  
  Northeast Normal University
  
  China
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 1, 2018, págs. 123-142
Idioma: inglés
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Resumen
- We study hom-Nijenhuis operators, T∗-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∗-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∗-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.