Higher-Dimensional Automorphic Lie Algebras

Vincent Knibbeler, Sara Lombardo*, Jan A. Sanders

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

The paper presents the complete classification of Automorphic Lie Algebras based on sln(C) , where the symmetry group G is finite and acts on sln(C) by inner automorphisms, sln(C) has no trivial summands, and where the poles are in any of the exceptional G-orbits in C¯. A key feature of the classification is the study of the algebras in the context of classical invariant theory. This provides on the one hand a powerful tool from the computational point of view; on the other, it opens new questions from an algebraic perspective (e.g. structure theory), which suggest further applications of these algebras, beyond the context of integrable systems. In particular, the research shows that this class of Automorphic Lie Algebras associated with the TOY groups (tetrahedral, octahedral and icosahedral groups) depend on the group through the automorphic functions only; thus, they are group independent as Lie algebras. This can be established by defining a Chevalley normal form for these algebras, generalising this classical notion to the case of Lie algebras over a polynomial ring.

Original languageEnglish
Pages (from-to)987-1035
Number of pages49
JournalFoundations of Computational Mathematics
Volume17
Issue number4
DOIs
Publication statusPublished - Aug 2017

Keywords

  • Automorphic Lie Algebras
  • Chevalley normal forms
  • Infinite-dimensional Lie algebras

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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