Representations of Dirichlet operator algebras

Irreducible Representations of Operator Algebras

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

Boundary Representations for Operator Algebras

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C-envelope.

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...