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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832556380920217600 |
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| author | Draen AdamoviĆ |
| author_facet | Draen AdamoviĆ |
| author_sort | Draen AdamoviĆ |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-1a4174f8c40e4bee96bcee6cfee543ea |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1a4174f8c40e4bee96bcee6cfee543ea2025-02-03T05:45:33ZengWileyInternational 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 |
| spellingShingle | Draen AdamoviĆ A construction of some ideals in affine vertex algebras International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | A construction of some ideals in affine vertex algebras |
| title_sort | construction of some ideals in affine vertex algebras |
| url | http://dx.doi.org/10.1155/S0161171203201058 |
| work_keys_str_mv | AT draenadamovic aconstructionofsomeidealsinaffinevertexalgebras AT draenadamovic constructionofsomeidealsinaffinevertexalgebras |