## Abstract

The complete structure of the Casimir WA_{N} algebras is shown to exist in such a way that the Casimir WA_{N} algebra is a kind of truncated type of ∞ algebra both in the primary and in the quadratic basis, first using the associativity conditions in the basis of primary fields and second using the Miura basis coming from the free field realization as a different basis. We can conclude that the Casimir WA_{N} algebra is a kind of truncated type of W_{∞} algebra, so it is clear from any construction of W_{∞} algebra that by putting infinite number of fields Ws with W_{s} > N to zero, we arrive at the Casimir WA_{N} algebra. We concentrated in this work only for the particular case of 5 algebra since this example gives us explicitly a method on how to deal with the general case N.

Original language | English |
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Article number | 1750121 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 14 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1 Sept 2017 |

### Bibliographical note

Publisher Copyright:© 2017 World Scientific Publishing Company.

## Keywords

- Conformal
- W symmetry

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