We study finite group actions on Leibniz algebras, define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology groups which makes it a graded zinbiel algebra.
The aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which control deformations of Hom-Leibniz algebras. The cohomology and the associated deformation theory for Hom-Leibniz algebras as developed here are also extended to equivariant context, under the presence of finite group actions on Hom-Leibniz algebras.
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