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This paper proves the extension of the rational vertex operator algebra in representations and fusion rules for coset structures.
In this paper, we determinate the structure of the coset vertex operator algebra C(Losp(1|2)̂(2,0),Losp(1|2)̂(1,0)⊗2). We prove that C(Losp(1|2)̂(2,0),Losp(1|2)̂(1,0)⊗2) is an extension of the rational vertex operator algebra L(c10,7, 0). Representations and fusion rules for C(Losp(1|2)̂(2,0),Losp(1|2)̂(1,0)⊗2) are also completely determined.
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Feng et al. (2025) studied this question.
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