  The Toroidal Lie algebras are n variable genaralizations of Affine Kac-Moody
Lie algebras. As in the affine Lie algebras there exists finite order auto=
morphisms corresponding to Dynkin diagram automorphisms. The fixed point sub=
algebras are called twisted toroidal Lie algebras. In this paper we construt
faithfull representations for the twisted toroidal Lie algebras (this includes
the non-twisted case also) useing methods developed by Lepowsky-Wilson [LW].
This construction recovers the result by Eswara Rao-Moody [EM] in the
homogeneous picture and by Yuly Billig [B1] in the principal picture. The
proofs given in this paper are much shorter than the above works. The results
for the twisted case are compleetly new.
