Elliptic Genus and Vertex Operator Algebras

Elliptic genus and vertex operator algebras

were also studied in [47]. It was conjectured in [47] that all these elliptic operators are rigid, generalizing the famous vanishing theorem of Atiyah-Hirzebruch for the Â-genus. There were several rather interesting proofs of these Witten’s conjectures (see [46], [8], [38], [41]). The one relevant to this paper is the proof given in [38], [39] where the main idea was to use the modular invaria...

Vertex Operator Algebras And

Let V be a vertex operator algebra. We construct a sequence of associative algebras A n (V) (n = 0; 1; 2; :::) such that A n (V) is a quotient of A n+1 (V) and a pair of functors between the category of A n (V)-modules which are not A n?1 (V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is r...

To Vertex Operator Algebras

In this exposition, we continue the discussions of Dong [D2] and Li [L]. We shall prove an S3-symmetry of the Jacobi identity, construct the contragredient module for a module for a vertex operator algebra and apply these to the construction of the vertex operator map for the moonshine module. We shall introduce the notions of intertwining operator, fusion rule and Verlinde algebra. We shall al...

Vertex operator algebras and operads

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, n-ary operations for all n greater than or equal to 0, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation show...

Codes and Vertex Operator Algebras