TITLE

On the Classification of Automorphic Lie Algebras

AUTHOR(S)
Lombardo, Sara; Sanders, Jan
PUB. DATE
November 2010
SOURCE
Communications in Mathematical Physics;Nov2010, Vol. 299 Issue 3, p793
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The problem of reduction of integrable equations can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of Automorphic Lie Algebras, beyond the context of integrable systems. In this paper it is shown that $${\mathfrak{sl}_{2}(\mathbb{C})}$$–based Automorphic Lie Algebras associated to the icosahedral group $${{\mathbb I}}$$, the octahedral group $${{\mathbb O}}$$, the tetrahedral group $${{\mathbb T}}$$, and the dihedral group $${{\mathbb D}_n}$$ are isomorphic. The proof is based on techniques from classical invariant theory and makes use of Clebsch-Gordan decomposition and transvectants, Molien functions and the trace-form. This result provides a complete classification of $${\mathfrak{sl}_{2}(\mathbb{C})}$$–based Automorphic Lie Algebras associated to finite groups when the group representations are chosen to be the same and it is a crucial step towards the complete classification of Automorphic Lie Algebras.
ACCESSION #
53505676

 

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