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Paper detail

Toroidal Z-Algebras

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.

preprint2012arXivOpen access
S. Eswara Rao
math.RT
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S. Eswara Rao

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