2009/09/21 by Masahiko Miyamoto, Miyamoto, Masahiko
Mathematics · #17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B69
paper · pdf · doi:10.48550/arxiv.0909.3665
14 pages, we avoid the calculations of fusion matrices, we need one assumption to avoid pseudo-trace function, and we also add a proof of the semisimplicity of orbifold models of rational VOAs
arxiv created 2010/07/28 · arxiv updated 2010/07/29
Let V be a simple C2-cofinite VOA of CFT-type and we assume that there is a simple module U such that \HomV(U\boxtimes V',V)\not=0 where V' is a restricted dual of V. As the author has shown, an S-transformation S(ΨV) of a trace function ΨV on V corresponding \beginpmatrix0&-1\cr 1&0\endpmatrix may contain pseudo-trace functions. Our assumption in this paper is that no pseudo-trace functions appear in S(ΨV). Under these assumptions, we prove that every V-module W is semirigid and ΨW appears in S(ΨV). As a corollary of our main theorem, a fixed point subVOA of a rational VOA of CFT-type by an automorphism of finite order becomes rational if fixed point subVOA is C2-cofinite.