W -algebras related to parafermion algebras

@article{Dong2008WR,
  title={W -algebras related to parafermion algebras},
  author={C. Dong and C. Lam and H. Yamada},
  journal={Journal of Algebra},
  year={2008},
  volume={322},
  pages={2366-2403}
}
  • C. Dong, C. Lam, H. Yamada
  • Published 2008
  • Mathematics
  • Journal of Algebra
  • Abstract We study a W-algebra of central charge 2 ( k − 1 ) / ( k + 2 ) , k = 2 , 3 , … , contained in the commutant of a Heisenberg algebra in a simple affine vertex operator algebra L ( k , 0 ) of type A 1 ( 1 ) with level k. We calculate the operator product expansions of the W-algebra. We also calculate some singular vectors in the case k ⩽ 6 and determine the irreducible modules and Zhu's algebra. Furthermore, the rationality and the C 2 -cofiniteness are verified for such k. 
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