Abstract
In this article, we compute the first space of cohomology of Vect (ℝ n|n ), the Lie superalgebra of vector fields on the supermanifold ℝ n|n with coefficients in 𝒻 (ℝ n|n ), the space of smooth functions on ℝ n|n . We give a super analog of the cohomologies of vector fields that where studied for instance by Fuchs [Citation2]. This work allows us to classify the deformations of the action of Vect(ℝ n|n ) on 𝒻 (ℝ n|n ).
ACKNOWLEDGMENTS
I would like to thank C. Roger and P. Lecomte for their suggestions and remarks.
Notes
Communicated by L. Small.