On integral forms for vertex algebras associated with affine Lie algebras and lattices

Abstract

We revisit the construction of integral forms for vertex (operator) algebras $V_L$ based on even lattices $L$ using generators instead of bases, and we construct integral forms for $V_L$-modules. We construct integral forms for vertex (operator) algebras based on highest-weight modules for affine Lie algebras and we exhibit natural generating sets. For vertex operator algebras in general, we give conditions showing when an integral form contains the standard conformal vector generating the Virasoro algebra. Finally, we study integral forms in contragredients of modules for vertex algebras.

25 pages, minor corrections and references added, now published online in the Journal of Pure and Applied Algebra

References in corpus (1)

• Applications of vertex algebra covering procedures to Chevalley groups and modular moonshine

Cited by in corpus (5)

• Integral forms for tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$ and their modules
• A Self-Dual Integral Form of the Moonshine Module
• Intertwining operators among modules for affine Lie algebra and lattice vertex operator algebras which respect integral forms
• Lattice structure of modular vertex algebras
• Monstrous Moonshine for integral group rings