Abstract
We show that automorphic Lie algebras which contain a Cartan subalgebra with a constant-spectrum, called hereditary, are completely described by 2-cocycles on a classical root system taking only two different values. This observation suggests a novel approach to their classification. By determining the values of the cocycles on opposite roots, we obtain the Killing form and the abelianization of the automorphic Lie algebra. The results are obtained by studying equivariant vectors on the projective line. As a byproduct, we describe a method to reduce the computation of the infinite-dimensional space of said equivariant vectors to a finite-dimensional linear computation and the determination of the ring of automorphic functions on the projective line.
Original language | English |
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Article number | 1950076 |
Journal | Communications in Contemporary Mathematics |
Volume | 22 |
Issue number | 8 |
Early online date | 20 Dec 2019 |
DOIs | |
Publication status | Published - Dec 2020 |
Funding
Sara Lombardo gratefully acknowledges the financial support from EPSRC (EP/E044646/1 and EP/E044646/2) and from NWO VENI (016.073.026).
Funders | Funder number |
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Fundação para a Ciência e a Tecnologia | PTDC/FER-FIL/28442/2017 |
Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 016.073.026 |
Engineering and Physical Sciences Research Council | EP/E044646/1, EP/E044646/2 |
Keywords
- automorphic Lie algebras
- Rational equivariant vectors