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

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

1996-05-21

arxiv.org/abs/q-alg/9605032v1

Mathematics

Quantum Algebra

Latex 17 pages

Scientific paper

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.

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