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Open Access Publications from the University of California

Representations of Vertex Operator Algebras

  • Author(s): Yu, Nina
  • Advisor(s): Dong, Chongying
  • et al.

In this thesis we study the representation theory of vertex operator algebras. The thesis consists of two parts. The first part deals with the connection among rationality, regularity and $C_2$-cofiniteness of vertex operator algebras. It is proved that if any $Z$-graded weak module for a vertex operator algebra V is completely reducible, then V is rational and $C_2$-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras. Motivated by classification of rational vertex operator algebras with central charge c = 1. We compute the quantum dimensions of irreducible modules of the rational and C2-cofinite vertex operator algebra $V_{L_2}^{A_4}$ in the other part.This result will be used to determine the fusion rules for this algebra.

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