engleski

Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type $A$.

Let $L(-\frac{;1};{;2};(l+1), 0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{;l};^{;(1)};$ with the lowest admissible half-integer level $-\frac{;1};{;2};(l+1)$, for even~$l$. We study the category of weak modules for that vertex operator algebra which are in category $\cal{;O};$ as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.

vertex operator algebra; affine Kac-Moody algebra

nije evidentirano