Abstract
In this paper the W-algebra W(2, 2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to an irreducible highest weight W(2, 2)- module or a tensor product of two simple Virasoro vertex operator algebras. Furthermore, we show that any rational, C 2-cofinite and simple vertex operator algebra whose weight 1 subspace is zero, weight 2 subspace is 2-dimensional and with central charge c = 1 is isomorphic to \({L(\frac{1}{2},0)\otimes L(\frac{1}{2},0)}\).
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Communicated by Y. Kawahigashi
Supported by NSF grants and a research grant from the Committee on Research, UC Santa Cruz.
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Zhang, W., Dong, C. W-Algebra W(2, 2) and the Vertex Operator Algebra \({L(\frac{1}{2},\,0)\,\otimes\, L(\frac{1}{2},\,0)}\) . Commun. Math. Phys. 285, 991–1004 (2009). https://doi.org/10.1007/s00220-008-0562-x
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DOI: https://doi.org/10.1007/s00220-008-0562-x