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theses

We study integral forms in vertex operator algebras over $mathbb{C}$. We prove general results on when a multiple of the standard conformal vector $omega$ can be added to an integral form of a vertex operator algebra and when intertwining operators among modules for a vertex operator algebra respect integral forms in the modules. We also show when the $mathbb{Z}$-dual of an integral form in a module for a vertex operator algebra is an integral form in the contragredient module. As examples, we consider vertex operator algebras based on affine Lie algebras and even lattices, and tensor powers of the Virasoro vertex operator algebra $L(frac{1}{2},0)$. In particular, we demonstrate vertex algebraic generators of integral forms for standard modules for affine Lie algebras that were first constructed in work of Garland; we reprove Borcherds' construction of integral forms in lattice conformal vertex algebras using generators; and we find generating sets that include $omega$ for integral forms in tensor powers $L(frac{1}{2},0)^{otimes n}$ when $nin 4mathbb{Z}$. We also construct integral forms in modules for these vertex operator algebras using generating sets, and we show when intertwining operators among modules for these vertex operator algebras respect integral forms in the modules.

ETD_5425

Ph.D.

Includes bibliographical references

by Robert H. McRae

doi:10.7282/T3KS6PV2

ETD doctoral

The author owns the copyright to this work.