This paper is concerned with studying necessary and sufficient conditions on a ring [italic]R such that for certain classes of right [italic]R-modules, the singular submodule of any member of the class is a direct summand of the module. The classes of interest are the class of a…
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural …
The main axiom for a vertex operator algebra (over a field of characteristic zero), the Jacobi identity, is extended to multi-operator identities. Then relative [bold capital]Z₂-twisted vertex operators are introduced and a Jacobi identity for these operators is established. The…
