Vertex operator algebras and modular invariance
Masahiko Miyamoto · Contemporary mathematics - American Mathematical Society · 2020
This is a survey about the modular invariance properties on vertex operator algebras. We restrict our subjects which have very close relationships with the original work by Zhu. As extensions of his result, many results related to modular invariance on orbifold theory, vector-valued modular forms and modular differential equations are well-known. We can also generalize them into weak Jacobi forms defined on weight one subspace of vertex operator algebra and also multi-variable functions defined on Jordan subalgebras of weight two subspace. We show that even in these extensions, some modular invariance property comes from the structure of vertex operator algebras.