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

Details W-algebra W(2,2) and the vertex operator algebra L(1/2,0)\otimes L(1/2,0) W-algebra W(2,2) and the vertex operator algebra L(1/2,0)\otimes L(1/2,0)

2007-11-28

arxiv.org/abs/0711.4624v1

Mathematics

Quantum Algebra

15 pages

Scientific paper

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, C_2-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)\otimes L(1/2,0).

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