2009/06/08 by Masahiko Miyamoto, Miyamoto, Masahiko
Mathematics · Medicine · #17B69 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Quantum Algebra (math.QA) #math.QA #msc:17B69
paper · pdf · doi:10.48550/arxiv.0906.1407
17 pages, we weaken slightly the definition of semi-rigidity
openalex publication_date 2009/06/08 · arxiv created 2010/07/27 · arxiv updated 2010/07/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We study properties of a C2-cofinite vertex operator algebra of CFT type. If it is also rational and V'≅ V, then the rigidity of the tensor category of modules has been proved by Huang. When we treat an irrational C2-cofinite VOA, the rigidity is too strong, because it is almost equivalent to be rational as we see. We introduce a natural weaker condition "semi-rigidity". Under this condition, we prove the following results. For a projective cover P of a V-module V and a finitely generated V-module M, the projective cover of M is a direct summand of the tensor product P\boxtimes M defined by logarithmic intertwining operators. Using this result, we prove the flatness property of finitely generated modules for the tensor products, that is, if 0→ A→ B→ C→ 0 is exact then so is 0→ D\boxtimes A→ D\boxtimes B→ D\boxtimes C→ 0 for any finitely generated V-modules A, B, C and D. As a corollary, we have that if a semi-rigid C2-cofinite V contains a rational subVOA with the same Virasoro element, then V is rational.