Commutative $C^{\ast }$-algebras generated by Toeplitz operators on the super unit ball

We extend known results about commutative $C^{\ast }$-algebras generated Toeplitz operators over the unit ball to the supermanifold setup. This is obtained by constructing commutative $C^{\ast }$-algebras of super Toeplitz operators over the super ball ${\mathbb{B}}^{p\mathrm{\mid }q}$ and the super Siegel domain ${\mathbb{U}}^{p\mathrm{\mid }q}$ that naturally generalize the previous results for the unit ball and the Siegel domain. In particular, we obtain one such commutative $C^{\ast }$-algebra for each even maximal Abelian subgroup of automorphisms of the super ball.