Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory

Chao Yang; Yiyi Zhu

doi:10.1016/j.jalgebra.2026.05.028

paper

Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory

arXiv:2511.06420 · doi:10.1016/j.jalgebra.2026.05.028

Abstract

Let $V$ be a vertex operator algebra equipped with two commuting finite-order automorphisms $g_{1}$ and $g_{2}$ , and set $g_{3} = g_{1} g_{2}$ . For $k = 1, 2, 3$ , let $W^{k}$ be a $g_{k}$ -twisted $V$ -module. Assuming that $W^{1}$ and $W^{2}$ are $C_{1}$ -cofinite and that there exists a surjective twisted logarithmic intertwining operator of type $(W ^{1} W ^{2} W ^{3})$ , we prove that $W^{3}$ is also $C_{1}$ -cofinite. The cofiniteness follows from the finite-dimensionality of the solution space of an associated complex-coefficient linear differential equation. As an application, under the condition of $C_{1}$ -cofiniteness, we establish the finiteness of the fusion rules and construct the fusion product.

27 pages