A construction of some ideals in affine vertex algebras
Abstract
Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k} (\g)$, and a family $V_{m,n} (\g)$ of quotient VOAs. These families include VOAs associated to the integrable representations, and VOAs associated to admissible representations at half-integer levels investigated in q-alg/9502015. We also explicitly identify the Zhu's algebras $A(V_{m,n} (\g))$ and find a connection between these Zhu's algebras and Weyl algebras.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2001
- DOI:
- 10.48550/arXiv.math/0103006
- arXiv:
- arXiv:math/0103006
- Bibcode:
- 2001math......3006A
- Keywords:
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- Quantum Algebra;
- 17B69;
- 17B67
- E-Print:
- 10 pages, Latex, minor changes