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Rankin-Cohen algebras and commutative associative sl_2-algebras

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NC2W02 - Crossing the bridge: New connections in number theory and physics

We talk about RC algebras, which are modeled on spaces of classical modular forms equipped with the well-known Rankin-Cohen brackets. We construct a commutative associative algebra out of any two RC algebras and then, by specializing one of them, obtain equivalencesof categories between the category of RC algebras and suitable categories of commutative associative algebras together with an action of the Lie algebra sl_2 by derivations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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