Certain associative algebras similar to U(sl2) and Zhu's algebra A(VL)

Chongying Dong; Haisheng Li; Geoffrey Mason

doi:10.1006/jabr.1997.7112

Certain associative algebras similar to U(sl₂) and Zhu's algebra A(V_L)

Chongying Dong, Haisheng Li, Geoffrey Mason

Rutgers Camden, Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	532-551
Number of pages	20
Journal	Journal of Algebra
Volume	196
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1997.7112
State	Published - Oct 15 1997

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1006/jabr.1997.7112

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

author = "Chongying Dong and Haisheng Li and Geoffrey Mason",

note = "Funding Information: * Supported by NSF Grant DMS-9303374 and a research grant from the Committee on Research, UC Santa Cruz. ²Current address: Department of Mathematical Science, Rutgers University, Camden, NJ 08102. ³Supported by NSF Grant DMS-9401272 and a research grant from the Committee on Research, UC Santa Cruz.",

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N2 - It is proved that Zhu's algebra for the vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of a certain associative algebra introduced by Smith. Zhu's algebra for the vertex operator algebra associated to any positive-definite even lattice is also calculated and is related to a generalization of Smith's algebra.

AB - It is proved that Zhu's algebra for the vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of a certain associative algebra introduced by Smith. Zhu's algebra for the 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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Certain associative algebras similar to U(sl₂) and Zhu's algebra A(V_L)

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