# Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A - Mathematics > Quantum Algebra

Abstract: Let $L-{1-2}l+1,0$ be the simple vertex operator algebra associated to anaffine Lie algebra of type $A {l}^{1}$ with the lowest admissiblehalf-integer level $-{1-2}l+1$, for even l. We study the category of weakmodules for that vertex operator algebra which are in category $\cal{O}$ asmodules for the associated affine Lie algebra. We classify irreducible objectsin that category and prove semisimplicity of that category.

Author: Ozren Perse

Source: https://arxiv.org/