Smash product construction of modular lattice vertex algebras

Abstract

Motivated by a work of Li, we study nonlocal vertex algebras and their smash products over fields of positive characteristic. Through smash products, modular vertex algebras associated with positive definite even lattices are reconstructed. This gives a different construction of the modular vertex algebras obtained from integral forms introduced by Dong and Griess in lattice vertex operator algebras over a field of characteristic zero.

Keywords

• vertex operator algebra
• modular vertex algebra