What is the Zhu's algebra for Heisenberg VOA

27 Views Asked by At

I am reading Zhu's famous paper "Modular Invariance and vertex operator algebra". In this paper, Zhu associates each vertex operator algebra with an unital associative algebra, so-called the Zhu's algebra. He proved the one-one correspondence between VOA's module and zhu's algebra's module. I would like to give a simple example for this theorem. I think Heisenberg algebra may be the simplest VOA that I can recall.