Let be a finite-dimensional simple Lie algebra and let be the simple affine vertex operator algebra associated to at a level such that , where is the dual Coxeter number of . We explain how to use recent results on braided tensor categories to show that the category of -cofinite L_k(\mathfrak{g})\mathfrak{g}k\mathfrak{g}C_1L_k(\mathfrak{g})\mathfrak{g}\mathfrak{g}$ at different levels.
Semisimplicity of ordinary modules for simple affine vertex operator algebras at positive rational shifted levels Sponsored by the Meyer Fund
Semisimplicity of ordinary modules for simple affine vertex operator algebras at positive rational shifted levels