Toroidal Z-Algebras
Abstract
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.
Cite
@article{arxiv.math/0402134,
title = {Toroidal Z-Algebras},
author = {S. Eswara Rao},
journal= {arXiv preprint arXiv:math/0402134},
year = {2012}
}
Comments
Many misprints are corrected