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

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 o...

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Bibliographic Details
Published in:	Journal of geometry and physics Vol. 146; p. 103488
Main Authors:	Imed, Basdouri, Mabrouk, Ben Nasr, Sami, Chouaibi, Hassen, Mechi
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-12-2019
Subjects:	[formula omitted]-supertransvectants Modular forms Rankin–Cohen brackets Supermodular forms Transvectants Supermodular forms Transvectants Modular forms 1\|1-supertransvectants Rankin–Cohen brackets
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Summary:	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.
ISSN:	0393-0440 1879-1662
DOI:	10.1016/j.geomphys.2019.103488