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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Main Author: Draen AdamoviĆ
Format: Article
Language:English
Published: Wiley 2003-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171203201058
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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.
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publishDate 2003-01-01
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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