Vertex operator algebras associated to modular invariant representations for $A_1 ^{(1)}$

Vertex operator algebras associated to modular invariant representations for A ( 1 ) 1 ∗

We investigate vertex operator algebras L(k, 0) associated with modular-invariant representations for an affine Lie algebra A (1) 1 , where k is ’admissible’ rational number. We show that VOA L(k, 0) is rational in the category O and find all irreducible representations in the category of weight modules.

Vertex operator algebras associated to admissible representations of ŝl 2

Let {e, f, h} be a standard basis for g = sl2 such that [e, f ] = h, [h, e] = 2e, [h, f ] = −2f , ĝ the corresponding affine Lie algebra and L(l, j) the irreducible highest weight ĝ-module of level l with highest weight j. It is well known that the vacuum representation L(l, 0) has a natural vertex operator algebra (or chiral algebra) structure for any l 6= −2 (cf. [FZ]). If l is a positive int...

Representations of vertex operator algebras

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

Representations of Ternary Code Vertex Operator Algebras

Twisted Representations of Vertex Operator Algebras

Let V be a vertex operator algebra and g an automorphism of finite order. We construct an associative algebra Ag(V ) and a pair of functors between the category of Ag(V )-modules and a certain category of admissible g-twisted V -modules. In particular, these functors exhibit a bijection between the simple modules in each category. We give various applications, including the fact that the comple...