On the Gelfand-Kirillov conjecture for the W-algebras attached to the minimal nilpotent orbits

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• 作者：Alexey Petukhov¹ ; ^{alex--2@yandex.ru" class="auth_mail" title="E-mail the corresponding author}
• 关键词：W-algebra ; Gelfand&ndash ; Kirillov conjecture ; Noncommutative localization
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：470
• 期：Complete
• 页码：289-299
• 全文大小：307 K

文摘

Consider the W-algebra H   attached to the minimal nilpotent orbit in a simple Lie algebra g$\mathfrak{g}$ over an algebraically closed field of characteristic 0. We show that if an analogue of the Gelfand–Kirillov conjecture holds for such a W-algebra, then it holds for the universal enveloping algebra U(g)$\mathrm{U}(\mathfrak{g})$. This, together with a result of A. Premet, implies that the analogue of the Gelfand–Kirillov conjecture fails for some W  -algebras attached to the minimal nilpotent orbit in Lie algebras of types B_n$B_n$(n≥3)$(n\ge 3)$, D_n$D_n$(n≥4)$(n\ge 4)$, E₆,E₇,E₈$E_6,E_7,E_8$, and F₄$F_4$.