Lam, Ching Hung Construction of vertex operator algebras from commutative associative algebras. (English) Zbl 0892.17020 Commun. Algebra 24, No. 14, 4339-4360 (1996). 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. Reviewer: Dražen Adamović (Zagreb) Cited in 1 ReviewCited in 8 Documents MSC: 17B69 Vertex operators; vertex operator algebras and related structures 17B68 Virasoro and related algebras 17B65 Infinite-dimensional Lie (super)algebras Keywords:commutative algebra; vertex operator algebra; tensor products; Virasoro vertex operator algebra × Cite Format Result Cite Review PDF 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.