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Modular Hecke algebras over Mobius categories

Banerjee, Abhishek (2018) Modular Hecke algebras over Mobius categories. In: JOURNAL OF GEOMETRY AND PHYSICS, 131 . pp. 23-40.

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Official URL: https://dx.doi.org/10.1016/j.geomphys.2018.04.008


We extend the modular Hecke operators of Connes and Moscovici by taking values in the modular incidence algebra MC] over a Mobius category C. Here M is the `modular tower' consisting of all modular forms of all weights across all levels. We construct multiple product structures on the collection A(Gamma)C] of modular Hecke operators of level Gamma over C, where Gamma is a principal congruence subgroup. These product structures are then shown to be well behaved with respect to Hopf actions on A(Gamma)C]. While A(Gamma)C] already carries an action of the Hopf algebra H-1 of codimension 1-foliations, the noncommutativity of the modular incidence algebra MC] allows us to construct additional operators on A(Gamma)C]. The use of Mobius categories provides a single framework for describing modular Hecke operators taking values in various rings: from formal power series rings over M to arithmetic functions over M and algebras of upper triangular matrices with entries in M. Moreover, we use functors between Mobius categories to study relations between various modular Hecke algebras. (C) 2018 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: Copyright of this article belong to ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 30 Jul 2018 14:40
Last Modified: 30 Jul 2018 14:40
URI: http://eprints.iisc.ac.in/id/eprint/60313

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