W-algebra W(2,2) and the vertex operator algebra L(1/2,0)⊗ L(1/2,0)

2007/11/28 by Zhang, W., Dong, C. · 1 citation
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0711.4624

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 a highest irreducible W(2,2)-module or a tensor product of two irreducible Virasoro vertex operator algebras. Furthermore, any rational, C₂-cofinite simple vertex operator algebra whose weight 1 subspace is zero and weight 2 subspace is 2-dimensional, and with central charge c=1 is isomorphic to L(1/2,0)⊗ L(1/2,0).

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