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Mosc. Math. J., 2004, Volume 4, Number 1, Pages 111–130 (Mi mmj144)  

This article is cited in 48 scientific papers (total in 48 papers)

Rankin-Cohen brackets and the Hopf algebra of transverse geometry

A. Connesa, H. Moscovicib

a Collège de France
b Ohio State University

Abstract: 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.

Key words and phrases: Rankin–Cohen brackets, modular Hecke algebras, Hopf symmetry, inner Schwarzian cocycle, quadratic differential, transverse fundamental class, Rankin–Cohen deformations of algebras.


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MSC: 11F32, 11F75, 58B34
Received: April 27, 2003

Citation: A. Connes, H. Moscovici, “Rankin-Cohen brackets and the Hopf algebra of transverse geometry”, Mosc. Math. J., 4:1 (2004), 111–130

Citation in format AMSBIB
\by A.~Connes, H.~Moscovici
\paper Rankin-Cohen brackets and the Hopf algebra of transverse geometry
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 1
\pages 111--130

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