Commutative C*-Algebras Generated by Toeplitz Operators on the Super Unit Ball

Abstract

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