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

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, 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).

15 pages

Cited by in corpus (8)

• The (super)conformal BMS${}_3$ algebra
• The derivations, central extensions and automorphism group of the Lie algebra $W$
• Whittaker Modules For The W-algebra W(2,2)
• Lie bialgebra structures on the $W$-algebra W(2,2)
• Higher-order Galilean contractions
• Derivations and automorphism groups of the original deformative Schrödinger-Virasoro algebras
• Quantum group structure of the q-deformed $W$ algebra $\WW_q$
• Whittaker Modules for Graded Lie Algebras