Extended super-Kač-Moody algebras and their super-derivation algebras

@article{Coquereaux1990ExtendedSA,
  title={Extended super-Ka{\vc}-Moody algebras and their super-derivation algebras},
  author={Robert Coquereaux and Luc Frappat and Eric Ragoucy and P. Sorba},
  journal={Communications in Mathematical Physics},
  year={1990},
  volume={133},
  pages={1-35}
}
We study theN-extended super-Kač-Moody algebras, i.e. extensions of the Lie algebra of the loop group over the super-circleAN. The extensions are characterized by 2-cocycles which are computed in terms of the cyclic cohomology of the Grassmann algebra withN generators. The graded algebra of super-derivations compatible with each extension is determined. The casesN=1,2,3 are examined in detail and their relation with the Ademollo et al. superconformal algebras is discussed. We examine the… 
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