Poisson Deformed Super-Algebras and Moyal Quantization

The procedure to obtain the semi-classical limit of Lie-Hopf and quantum algebras introduced in preceding papers has been extended to Lie and quantum super-algebras. With a different definition of the limit the approach is the same: an h-depending family of Hopf super-algebras is constructed starting from the super-bialgebra; then the singular limit h → 0 allows to move from quantum to semi-classical framework in the spirit of Moyal quantization. The Poisson undeformed ospP(1|2) and deformed ospPq(1|2) super-algebras are exhibited, both as a paradigmatic example and because of their interest in applications.