Commutative $C^*$-algebras generated by Toeplitz operators on the super unit ball

摘要

We extend known results about commutative $C^*$-algebras generated Toeplitzoperators over the unit ball to the supermanifold setup. This is obtained byconstructing commutative $C^*$-algebras of super Toeplitz operators over thesuper ball $\mathbb{B}^{p|q}$ and the super Siegel domain $\mathbb{U}^{p|q}$that naturally generalize the previous results for the unit ball and the Siegeldomain. In particular, we obtain one such commutative $C^*$-algebra for eacheven maximal Abelian subgroup of automorphisms of the super ball.