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Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice$L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of$L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of$\theta$. We classify the irreducible weak $V_{L}^{+}$-modules and show thatany irreducible weak $V_{L}^{+}$-module is isomorphic to a weak submodule ofsome irreducible weak $V_{L}$-module or to a submodule of some irreducible$\theta$-twisted $V_{L}$-module.

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 $2$