Rationality, Regularity, and C_2-cofiniteness

Abstract

We demonstrate that, for CFT vertex operator algebras, C_2-cofiniteness and rationality is equivalent to regularity. In addition, we show that, for C_2-cofinite vertex operators algebras, irreducible weak modules are ordinary modules and C_2-cofinite, and V_L^+ are C_2-cofinite.

latex, 15 pages

References in corpus (1)

• Modular invariance of trace functions in orbifold theory

Cited by in corpus (10)

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• Duality of subregular W-algebras and principal W-superalgebras
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• Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
• The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
• Q-systems and extensions of completely unitary vertex operator algebras
• Rationality of the exceptional W-algebras ${\mathcal{W}}_k({\mathfrak{sp}}_4,f_{subreg})$ associated with subregular nilpotent elements of ${\mathfrak{sp}}_4$
• On semisimplicity of module categories for finite non-zero index vertex operator subalgebras
• 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 $2$ (Part $1$)
• Regular vertex operator subalgebras and compressions of intertwining operators