2025/11/03 by Shijie Cao, Jiancai Sun, Cao, Shijie +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2511.01474
We investigate a question posed by Gaberdiel and Gannon concerning the relationship between C2-algebras and twisted modules. To each twisted module W of a vertex algebra V, we first associate a decreasing sequence of subspaces \EnT(W)\n∈ℤ and demonstrate that the associated graded vector space grET(W) is a twisted module of vertex Poisson algebra grET(V). We introduce another decreasing sequence of subspace \CnT(W)\_n∈ℤ≥2 and establish a connection between \EnT(W)\n∈ℤ and \CnT(W)\_n∈ℤ≥2. By utilizing the twisted module grET(W) of vertex Poisson algebra grET(V), we prove that for any twisted module W of a vertex algebra V, C2-cofiniteness implies Cn-cofiniteness for all n≥ 2. Furthermore, we employ grET(W) to study generating subspaces of (1)/(T)ℕ-graded twisted modules of lower truncated ℤ-graded vertex algebras.