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Construction of vertex operator algebras from commutative associative algebras. (English) Zbl 0892.17020

Let \(A\) be a commutative associative algebra. In the paper under review the author proves that there is a vertex operator algebra \(V\) with the weight two space \(V_2 \cong A\). In the case when \(A\) is semisimple, then the constructed vertex operator algebra \(V\) is isomorphic to the tensor product of a certain number of vertex operator algebras associated to the Virasoro algebra.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
17B68 Virasoro and related algebras
17B65 Infinite-dimensional Lie (super)algebras
Full Text: DOI

References:

[1] DOI: 10.1073/pnas.83.10.3068 · Zbl 0613.17012 · doi:10.1073/pnas.83.10.3068
[2] Dong C., Progress in math (1993)
[3] Dong C., On vertex operator algebras as ,sl2-module (1993)
[4] Frenkel I.B., Mem.Amer.Math.Soc 104 (1993)
[5] Frenkel I.B., Vertex operator algebras and the Monster (1988) · Zbl 0674.17001
[6] DOI: 10.1215/S0012-7094-92-06604-X · Zbl 0848.17032 · doi:10.1215/S0012-7094-92-06604-X
[7] DOI: 10.1007/BF01389186 · Zbl 0498.20013 · doi:10.1007/BF01389186
[8] DOI: 10.1080/00927879508825472 · Zbl 0836.17021 · doi:10.1080/00927879508825472
[9] Li H.S., vertex superalgebras and Modules 23 (1994)
[10] Lian B.H., On the classification of simple vertex operator algebras 23 (1992)
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