In this note, we prove that the universal affine vertex algebra associated with a simple Lie algebra is simple if and only if the associated variety of its unique simple quotient is equal to . We also derive an analogous result for the quantized Drinfeld-Sokolov reduction applied to the universal affine vertex algebra.
Dans cet article, nous démontrons que l’algèbre vertex affine universelle associée à une algèbre de Lie simple est simple si et seulement si la variété associée à son unique quotient simple est égale à . Nous en déduisons un résultat analogue pour la réduction quantique de Drinfeld-Sokolov appliquée à l’algèbre vertex affine universelle.
@article{JEP_2021__8__169_0, author = {Tomoyuki Arakawa and Cuipo Jiang and Anne Moreau}, title = {Simplicity of vacuum modules and associated~varieties}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {169--191}, publisher = {\'Ecole polytechnique}, volume = {8}, year = {2021}, doi = {10.5802/jep.144}, mrnumber = {4201804}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.144/} }
TY - JOUR TI - Simplicity of vacuum modules and associated varieties JO - Journal de l’École polytechnique — Mathématiques PY - 2021 DA - 2021/// SP - 169 EP - 191 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.144/ UR - https://www.ams.org/mathscinet-getitem?mr=4201804 UR - https://doi.org/10.5802/jep.144 DO - 10.5802/jep.144 LA - en ID - JEP_2021__8__169_0 ER -
Tomoyuki Arakawa; Cuipo Jiang; Anne Moreau. Simplicity of vacuum modules and associated varieties. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 169-191. doi : 10.5802/jep.144. https://jep.centre-mersenne.org/articles/10.5802/jep.144/
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