Automorphic Lie algebras and modular forms
We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Let Γ be a finite index subgroup of SL(2,Z) with an action on a complex simple Lie algebra g, which can be extended to SL(2,C). We show that the Lie algebra of the corresponding g-valued modular forms is isomorphic to the extension of g over the usual modular forms. This establishes a modular analogue of a well-known result by Kac on twisted loop algebras. The case of principal congruence subgroups Γ(N),N≤6, is considered in more detail in relation to the classical results of Klein and Fricke and the celebrated Markov Diophantine equation. We finish with a brief discussion of the extensions and representations of these Lie algebras. [See full text paper for actual mathematical formulae.]
INVARIANT ALGEBRAS IN HYPERBOLIC GEOMETRY
Engineering and Physical Sciences Research CouncilFind out more...
Geometry and integrability
Russian Science FoundationFind out more...
- Mathematical Sciences
Published inInternational Mathematics Research Notices
PublisherOxford University Press
- VoR (Version of Record)
Rights holder© The Authors
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