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INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.14, no.9, 2017 (SCI-Expanded)
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 W-infinity 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-infinity algebra, so it is clear from any construction of W-infinity algebra that by putting infinite number of fields W-s with s > N to zero, we arrive at the Casimir WA(N) algebra. We concentrated in this work only for the particular case of WA(5) algebra since this example gives us explicitly a method on how to deal with the general case N.