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 -modules is a semisimple rigid braided tensor category. For certain levels, is known to be the same as the universal affine vertex operator algebra of and level , so in these cases, it follows that all generalized Verma modules induced from finite-dimensional simple -modules are simple, and the category of -cofinite is equivalent to a minor modification of the tensor category of finite-dimensional -modules. This makes it possible to construct many new vertex operator algebras by extending tensor products of affine vertex operator algebras associated to 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