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The PT-symmetry breaking, consistent hamiltonian interactions in all $n\geq4$ spacetime dimensions that can be added to an abelian BF model involving aset of scalar fields, two sorts of one-forms, and a system of two-forms areobtained by means of the hamiltonian deformation procedure based on local BRSTcohomology. This paper enhances one of our previous works, where onlyPT-invariant deformations were considered. The associated coupled theory is aninteracting, topological BF model exhibiting an open gauge algebra and on-shellreducibility relations.Comment: 22 page

PT-SYMMETRY BREAKING HAMILTONIAN INTERACTIONS IN BF MODELS