Hereditary automorphic Lie algebras

Vincent Knibbeler*, Sara Lombardo, Jan A. Sanders

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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 languageEnglish
Article number1950076
JournalCommunications in Contemporary Mathematics
Volume22
Issue number8
Early online date20 Dec 2019
DOIs
Publication statusPublished - 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).

FundersFunder number
Fundação para a Ciência e a TecnologiaPTDC/FER-FIL/28442/2017
Nederlandse Organisatie voor Wetenschappelijk Onderzoek016.073.026
Engineering and Physical Sciences Research CouncilEP/E044646/1, EP/E044646/2

    Keywords

    • automorphic Lie algebras
    • Rational equivariant vectors

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