Rationality of the vertex algebra $V_L^{+}$ when $L$ is a nondegenerate even lattice of arbitrary rank

Abstract

In this paper we prove that the vertex algebra $V_L^{+}$ is rational if $L$ is a negative definite even lattice of finite rank, or if $L$ is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative definite. In particular, for such even lattices $L$, we show that the Zhu algebras of the vertex algebras $V_L^{+}$ are semisimple. This extends the result of Abe which establishes the rationality of $V_L^{+}$ when $L$ is a positive definite even lattice of finite rank.

References in corpus (1)

• Rationality of vertex operator algebras

Cited by in corpus (1)

• The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order $2$ (Part $1$)