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 \({\mathbb{B}^{p|q}}\) and the super Siegel domain \({\mathbb{U}^{p|q}}\) that naturally generalize the previous results for the unit ball and the Siegel domain. In particular, we obtain one such commutative C*-algebra for each even maximal Abelian subgroup of automorphisms of the super ball.
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The authors were supported by SNI and Conacyt grants.
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Quiroga-Barranco, R., Sánchez-Nungaray, A. Commutative C*-Algebras Generated by Toeplitz Operators on the Super Unit Ball. Adv. Appl. Clifford Algebras 26, 363–397 (2016). https://doi.org/10.1007/s00006-015-0593-2
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DOI: https://doi.org/10.1007/s00006-015-0593-2