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We address the problem of determining the obstruction to existence of solutions of the hexagon equation for abelian fusion rules and the classification of prime abelian anyons. Given an abelian group A we will denote by S 2 (A), ∧ 2 A and A ⊗2 the second symmetric power, second exterior power and second tensor power of A, respectively. Here, we see A as a Z-module.doi:10.15446/recolma.v50n2.62213 fatcat:5l2vaph5d5ejngphlo3kxseazy