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For every m ∈ ℂ ∖ 0, −2 and every nonnegative integer k we define the vertex operator (super)algebra D m,k having two generators and rank
. If m is a positive integer then D m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.
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