Affine Lie algebras and vertex operator algebras

1993 ◽  
pp. 141-160
Author(s):  
Chongying Dong ◽  
James Lepowsky
Keyword(s):  
Lie Algebras ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Affine Lie Algebras

scholarly journals A construction of some ideals in affine vertex algebras

2003 ◽  
Vol 2003 (15) ◽  
pp. 971-980 ◽  
Author(s):  
Dražen AdamoviĆ
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Affine Lie Algebras ◽  
Explicit Formulas ◽  
Singular Vectors ◽  
Weyl Algebras ◽  
New Family

We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of typesAandC. 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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