Title: Projectively Equivariant Quantizations over the Superspace $${\mathbb{R}^{p|q}}$$
Abstract: We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra $${\mathfrak{pgl}(p+1|q)}$$ is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of $${\mathfrak{pgl}(n|n)\not\cong \mathfrak{sl}(n|n)}$$ ), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.