Lattice vertex superalgebras and their modules over fields of prime characteristic

2026/07/24 by Hongju Zhao, H. W. Zhao, Qiang Mu
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Rings, Modules, and Algebras

paper · doi:10.1112/jlms.70653

Abstract

Abstract 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 .

Citations

• On integral forms for vertex algebras associated with affine Lie algebras and lattices
• Symmetric invariant bilinear forms on vertex operator algebras
• Local systems of vertex operators, vertex superalgebras and modules
• Integral forms in vertex operator algebras which are invariant under finite groups
• Lattice vertex algebras over fields of prime characteristic
• Lattice-integrality of certain group-invariant integral forms in vertex operator algebras
• Determinants for integral forms in lattice type vertex operator algebras
• Vertex superalgebras over fields of prime characteristic
• Representations of vertex operator superalgebras over an arbitrary field

Related

• Representations of vertex operator superalgebras over an arbitrary field
• Representations of a class of lattice type vertex algebras
• Some remarks on associated varieties of vertex operator superalgebras
• Semi-conformal structure on certain vertex superalgebras associated to vertex superalgebroids
• Vertex Operator Superalgebras and Their Representations