  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.
