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In this article, we give Maurer-Cartan characterizations of equivariant Liesuperalgebra structures. We introduce equivariant cohomology and equivariantformal deformation theory of Lie superalgebras. As an application ofequivariant cohomology we study the equivariant formal deformation theory ofLie superalgebras. As another application we characterize equivariant centralextensions of Lie superalgebras using second equivariant cohomology. We givesome examples of Lie superalgebras with an action of a group and equivariantformal deformations of a classical Lie superalgebras.

Maurer-Cartan characterization, cohomology and deformations of equivariant Lie superalgebras