Cohomology of Hom-Leibniz and $n$-ary Hom-Nambu-Lie superalgebras
  The aim of this paper is to study the cohomology of Hom-Leibniz superalgebras. We construct the $q$-deformed Heisenberg-Virasoro superalgebra of Hom-type and provide as application the computations of the derivations and second cohomology group. Moreover, we extend to graded case the Takhtajan's construction of a cohomology of $n$-ary Hom-Nambu-Lie algebras starting from cohomology of Hom-Leibniz algebras. 
El Kadri Abdaoui, Sami Mabrouk and Abdenacer Makhlouf
math.RT math.RA