Certain associative algebras similar to $U(s{l}_2)$ and Zhu's algebra $A(V_L)$

Abstract

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

References in corpus (1)

• On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras

Cited by in corpus (1)

• First cohomologies of affine, Virasoro and lattice vertex operator algebras