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Action of Hopf on the twisted modular Hecke operator

Banerjee, Abhishek (2016) Action of Hopf on the twisted modular Hecke operator. In: JOURNAL OF NONCOMMUTATIVE GEOMETRY, 9 (4). pp. 1155-1173.

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Official URL: http://dx.doi.org/10.4171/JNCG/219


Let Gamma subset of SL2(Z) be a principal congruence subgroup. For each sigma is an element of SL2(Z), we introduce the collection A(sigma)(Gamma) of modular Hecke operators twisted by sigma. Then, A(sigma)(Gamma) is a right A(Gamma)-module, where A(Gamma) is the modular Hecke algebra introduced by Connes and Moscovici. Using the action of a Hopf algebra h(0) on A(sigma)(Gamma), we define reduced Rankin-Cohen brackets on A(sigma)(Gamma). Moreover A(sigma)(Gamma) carries an action of H 1, where H 1 is the Hopf algebra of foliations of codimension 1. Finally, we consider operators between the levels A(sigma)(Gamma), sigma is an element of SL2(Z). We show that the action of these operators can be expressed in terms of a Hopf algebra h(Z).

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the EUROPEAN MATHEMATICAL SOC, PUBLISHING HOUSE, E T H-ZENTRUM SEW A27, SCHEUCHZERSTRASSE 70, CH-8092 ZURICH, SWITZERLAND
Keywords: Modular Hecke algebras; Rankin-Cohen brackets; Hopf actions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 29 Feb 2016 06:47
Last Modified: 29 Feb 2016 06:47
URI: http://eprints.iisc.ac.in/id/eprint/53341

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