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.
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.
Accepté le :
Publié le :
DOI : 10.5802/jep.144
Keywords: Associated variety, affine Kac-Moody algebra, affine vertex algebra, singular vector, affine $W$-algebra
Mot clés : Variété associée, algèbre de Kac-Moody, algèbre vertex affine, vecteur singulier, $W$-algèbre affine
Tomoyuki Arakawa 1 ; Cuipo Jiang 2 ; Anne Moreau 3
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@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 AU - Tomoyuki Arakawa AU - Cuipo Jiang AU - Anne Moreau TI - Simplicity of vacuum modules and associated varieties JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 169 EP - 191 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.144/ DO - 10.5802/jep.144 LA - en ID - JEP_2021__8__169_0 ER -
%0 Journal Article %A Tomoyuki Arakawa %A Cuipo Jiang %A Anne Moreau %T Simplicity of vacuum modules and associated varieties %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 169-191 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.144/ %R 10.5802/jep.144 %G en %F JEP_2021__8__169_0
Tomoyuki Arakawa; Cuipo Jiang; Anne Moreau. Simplicity of vacuum modules and associated varieties. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 169-191. doi : 10.5802/jep.144. https://jep.centre-mersenne.org/articles/10.5802/jep.144/
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