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Rankin-Cohen brackets and associativity. (English) Zbl 1167.53075

D. Zagier introduced and discussed in [Proc. Indian Acad. Sci., Math. Sci. 104, No. 1, 57–75 (1994; Zbl 0806.11022)] a particular algebraic structure of the graded ring of modular forms, which is derived from the Rankin-Cohen brackets. In this paper, this structure is interpreted in terms of an associative deformation (star product) of this graded ring . More precisely, it is related to the Moyal star product on \({\mathbb C}^4\).

MSC:

53D55 Deformation quantization, star products
11F11 Holomorphic modular forms of integral weight
22E46 Semisimple Lie groups and their representations

Citations:

Zbl 0806.11022
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References:

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