Vertex operator algebras associated to modified regular representations of affine Lie algebras
| dc.creator | Zhu, Minxian | |
| dc.date | 2006-11-17 | |
| dc.date | 2007-11-20 | |
| dc.date.accessioned | 2026-07-07T08:43:50Z | |
| dc.date.available | 2026-07-07T08:43:50Z | |
| dc.description | Let $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$ be the affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertex operator algebras associated to $\mf g$. They are $\af \oplus \af$-modules of dual levels $k, \bar k \notin \Q$ in the sense that $k + \bar k = -2 h^\vee$ where $h^\vee$ is the dual Coxeter number of $\mf g$. Its conformal weight 0 component is the algebra of regular functions on $G$. This family of vertex operator algebras were previously studied by Arkhipov-Gaitsgory and Gorbounov-Malikov-Schechtman from different points of view. We show that the vertex envelope of the vertex algebroid associated to $G$ and level $k$ is isomorphic to the vertex operator algebra we constructed above when $k$ is irrational. The case of integral central charges is also discussed. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611517 | |
| dc.identifier | http://arxiv.org/abs/math/0611517 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142454 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B69, 17B67 | |
| dc.title | Vertex operator algebras associated to modified regular representations of affine Lie algebras | |
| dc.type | text |