Rankin-Cohen Brackets and the Hopf Algebra of Transverse Geometry

Details Rankin-Cohen Brackets and the Hopf Algebra of Transverse Geometry Rankin-Cohen Brackets and the Hopf Algebra of Transverse Geometry

2003-04-22

arxiv.org/abs/math/0304316v2

Mathematics

Quantum Algebra

29 pages; to appear in the Moscow Mathematical Journal (volume dedicated to Pierre Cartier)

Scientific paper

We settle in this paper a question left open in our paper ``Modular Hecke algebras and their Hopf symmetry'', by showing how to extend the Rankin-Cohen brackets from modular forms to modular Hecke algebras. More generally, our procedure yields such brackets on any associative algebra endowed with an action of the Hopf algebra of transverse geometry in codimension one, such that the derivation corresponding to the Schwarzian derivative is inner. Moreover, we show in full generality that these Rankin-Cohen brackets give rise to associative deformations.

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