Extensions of Tensor Products of Unitary Virasoro Vertex Operator Algebra

Abstract

Following the approach of [25 Miyamoto , M. ( 1998 ). Representation theory of code vertex operator algebras . J. Algebra 201 : 115 – 150 .[Crossref], [Web of Science ®] , [Google Scholar]], we construct a class of vertex operator (super)algebra 𝒲 D using some binary code D and irreducible modules of the unitary Virasoro vertex operator algebra . We also introduce a notion of induced modules and show that all irreducible 𝒲 D -modules are induced modules. In addition, we study the fusion rules and show that certain irreducible 𝒲 D modules are simple current modules.