Hereditary automorphic Lie algebras

Vincent Knibbeler*, Sara Lombardo, Jan A. Sanders

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number8
Publication statusPublished - 20 Dec 2020


  • automorphic Lie algebras
  • Rational equivariant vectors

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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