Local and Semilocal Vertex Operator Algebras

2004/09/21 by Chongying Dong, Geoffrey Mason
Mathematics · #math.QA #math.RT #msc:17B69

paper · pdf

published as J. Alg. 280 (2004), 350-366 · 17 pages

arxiv created 2004/09/21 · arxiv updated 2009/12/01

Abstract

We investigate a general structure theory for a vertex operator algebra. We discuss the center and blocks, the Jacobson radical and solvable radical and local vertex operator algebras. The main consequence of our structure theory is that if the vertex operator algebra satisfies some mild conditions then it is necessarily semilocal, i.e. a direct sum of local vertex operator algebras.

Related

• Some developments in vertex operator algebra theory, old and new
• A characterization of vertex operator algebras V_Zα⁺: I
• Introduction to vertex operator algebras I
• Unitary vertex operator algebras
• Irregular vertex algebras