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Abstract 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 3m{m + 2}. 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.
Dražen Adamović (Tue,) studied this question.