Higher-Dimensional Automorphic Lie Algebras

Higher-Dimensional Automorphic Lie Algebras The paper presents the complete classification of Automorphic Lie Algebras based on $${{\mathfrak {sl}}}_{n}(\mathbb {C})$$ sl n ( C ) , where the symmetry group G is finite and acts on $${{\mathfrak {sl}}}_n(\mathbb {C})$$ sl n ( C ) by inner automorphisms, $${{\mathfrak {sl}}}_n(\mathbb {C})$$ sl n ( C ) has no trivial summands, and where the poles are in any of the exceptional G-orbits in $$\overline{\mathbb {C}}$$ 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 $$\mathbb {T}\mathbb {O}\mathbb {Y}$$ T O Y 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Foundations of Computational Mathematics Springer Journals

Higher-Dimensional Automorphic Lie Algebras

Loading next page...
Springer US
Copyright © 2016 by The Author(s)
Mathematics; Numerical Analysis; Economics, general; Applications of Mathematics; Linear and Multilinear Algebras, Matrix Theory; Math Applications in Computer Science; Computer Science, general
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial