A construction of some ideals in affine vertex algebras
We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of types A and C. We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. These formulas generalize the ex...
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| Language: | English |
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Hindawi Limited
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203201058 |
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doaj-1a4174f8c40e4bee96bcee6cfee543ea2020-11-24T22:05:06ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-0120031597198010.1155/S0161171203201058A construction of some ideals in affine vertex algebrasDraen AdamoviĆ0Department of Mathematics, University of Zagreb, Bijenička 30, Zagreb 10 000, CroatiaWe study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of types A and C. We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. These formulas generalize the expressions for singular vectors from Adamović (1994). As a consequence, we obtain a new family of vertex operator algebras for which we identify the associated Zhu's algebras. A connection with the representation theory of Weyl algebras is also discussed.http://dx.doi.org/10.1155/S0161171203201058 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Draen AdamoviĆ |
| spellingShingle |
Draen AdamoviĆ A construction of some ideals in affine vertex algebras International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Draen AdamoviĆ |
| author_sort |
Draen AdamoviĆ |
| title |
A construction of some ideals in affine vertex algebras |
| title_short |
A construction of some ideals in affine vertex algebras |
| title_full |
A construction of some ideals in affine vertex algebras |
| title_fullStr |
A construction of some ideals in affine vertex algebras |
| title_full_unstemmed |
A construction of some ideals in affine vertex algebras |
| title_sort |
construction of some ideals in affine vertex algebras |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2003-01-01 |
| description |
We study ideals generated by singular vectors in vertex operator
algebras associated with representations of affine Lie algebras of types A and C. We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. These formulas generalize the expressions for singular vectors from Adamović (1994). As a consequence, we obtain a new family of vertex operator algebras for which we
identify the associated Zhu's algebras. A connection with the
representation theory of Weyl algebras is also discussed. |
| url |
http://dx.doi.org/10.1155/S0161171203201058 |
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