Construction of supermodular forms using differential operators from a given supermodular form

摘要

B.P. Cohen, Y. Manin and D. Zagier introduced the definition of supermodular form in Cohen et al. (1997). In the present paper, we also review the definition of supermodular form and we explicitly give answer to the following question: What differential operators do preserve supermodularity? These operators are supersymmetric generalization of Rankin-Cohen brackets. They are called Super Rankin-Cohen brackets. Finally, using the bijective correspondence between supermodular forms and superpseudodifferential operators invariants given by Cohen et al. (1997), we construct a star product involving the Super Rankin-Cohen brackets. (C) 2019 Elsevier B.V. All rights reserved.