Lattice vertex superalgebras and their modules over fields of prime characteristic

We study lattice vertex superalgebras over an algebraically closed field of prime characteristic using the integral form theory. We first use the integral forms of the lattice vertex superalgebra , denoted by (due to Dong and Griess), and of ‐modules, to characterize the modular lattice vertex superalgebra and its modules. More precisely, we provide the generating sets, obtain a bilinear form on , and determine the simplicity of and the irreducibility of ‐modules. Finally, we establish the complete reducibility of a specific family of lattice vertex superalgebras over when .