Reduction Groups and Automorphic Lie Algebras
Abstract
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 useful factorisations on two subalgebras similar to the factorisation of the current algebra on the positive and negative parts.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 August 2005
 DOI:
 10.1007/s0022000513345
 arXiv:
 arXiv:mathph/0407048
 Bibcode:
 2005CMaPh.258..179L
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 17B65;
 11F03;
 37K10
 EPrint:
 21 pages, standard LaTeX2e, corrected typos, accepted for publication in CMP  Communications in Mathematical Physics