Reduction Groups and Automorphic Lie Algebras

Details Reduction Groups and Automorphic Lie Algebras Reduction Groups and Automorphic Lie Algebras

2004-07-21

arxiv.org/abs/math-ph/0407048v2

Commun.Math.Phys. 258 (2005) 179-202

Physics

Mathematical Physics

21 pages, standard LaTeX2e, corrected typos, accepted for publication in CMP - Communications in Mathematical Physics

Scientific paper

10.1007/s00220-005-1334-5

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates the name automorphic Lie algebras. For automorphic Lie algebras we present bases in which they are quasigraded and all structure constants can be written out explicitly. These algebras have a useful factorisations on two subalgebras similar to the factorisation of the current algebra on the positive and negative parts.

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