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

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

2008-07-24

arxiv.org/abs/0807.3897v1

Mathematics

Quantum Algebra

Scientific paper

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.

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