2003/04/22 by Alain Connes, Connes, Alain, Henri Moscovici +1
Mathematics · #11F32 #11F75 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.NT #math.OA #math.QA #msc:11F32 #msc:11F75 #msc:58B34
paper · pdf · doi:10.48550/arxiv.math/0304316
29 pages; to appear in the Moscow Mathematical Journal (volume dedicated to Pierre Cartier)
openalex publication_date 2003/04/22 · arxiv created 2003/09/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.