Local and semilocal vertex operator algebras

We initiate a general structure theory for vertex operator algebras V. We discuss the center and the blocks of V, the Jacobson radical and solvable radical, and local vertex operator algebras. The main consequence of our structure theory is that if V satisfies some mild conditions, then it is necessarily semilocal, i.e., a direct sum of local vertex operator algebras. (C) 2004 Elsevier Inc. All rights reserved.