ℤ3symmetry and W3algebra in lattice vertex operator algebras

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Abstract
The W3 algebra of central charge 6/5 is realized as a subalgebra of the vertex operator algebra V√2A2 associated with a lattice of type √ 2A2 by using both coset construction and orbifold theory. It is proved that W3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.