Rationality of the vertex operator algebra $V_L^{+}$ for a positive definite even lattice $L$

Abstract

The lattice vertex operator algebra $V_L$ associated to a positive definite even lattice $L$ has an automorphism of order 2 lifted from -1-isometry of $L$. We prove that for the fixed point vertex operator algebra $V_L^{+}$, any ${\mathbb{Z}}_{\ge 0}$-graded weak modules is completely reducible.

30 pages, No figure

References in corpus (1)

• A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness