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...
 
/lp/springer_journal/higher-dimensional-automorphic-lie-algebras-l1EwP0rE0k
Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
Subject
Mathematics; Numerical Analysis; Economics, general; Applications of Mathematics; Linear and Multilinear Algebras, Matrix Theory; Math Applications in Computer Science; Computer Science, general
ISSN
1615-3375
eISSN
1615-3383
D.O.I.
10.1007/s10208-016-9312-1
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Foundations of Computational MathematicsSpringer Journals

Published: Apr 11, 2016

References

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 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

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

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off