Certain associative algebras similar to $U(sl_{2})$ and Zhu's algebra $A(V_{L})$

Dong, Chongying; Li, Haisheng; Mason, Geoffrey

Certain associative algebras similar to $U(sl_{2})$ and Zhu's algebra $A(V_{L})$

Authors

Dong, Chongying

Li, Haisheng

Mason, Geoffrey

Description

It is proved that Zhu's algebra for vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of certain associative algebra introduced by Smith. Zhu's algebra for vertex operator algebra associated to any positive-definite even lattice is also calculated and is related to a generalization of Smith's algebra.
Latex 17 pages