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

详细信息    查看全文

• 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 1" class="mathmlsrc">1-s2.0-S0021869316302733&_mathId=si1.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=4525d62567279ab7177c995a91390a94" title="Click to view the MathML source">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 12" class="mathmlsrc">1-s2.0-S0021869316302733&_mathId=si12.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=853f99312947f42bb6f611cd32272757" title="Click to view the MathML source">U(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 3" class="mathmlsrc">1-s2.0-S0021869316302733&_mathId=si3.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=7280b11349c623370a9ec43322e34ec4" title="Click to view the MathML source">B_n1-s2.0-S0021869316302733&_mathId=si4.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=a661fc5f8e99623c4810669730c0ca21" title="Click to view the MathML source">(n≥3)$(n\ge \mathrm{<font\; color="red">3</font>})$, 1-s2.0-S0021869316302733&_mathId=si5.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=cfc2d4aee9f76c4f1407e58d96f44261" title="Click to view the MathML source">D_n$D_n$1-s2.0-S0021869316302733&_mathId=si6.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=68106fb8b8a533f6ce121481f7a5d18a" title="Click to view the MathML source">(n≥4)$(n\ge 4)$, 1-s2.0-S0021869316302733&_mathId=si7.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=9235e5b0b8fe3a5ee083c27c9b053326" title="Click to view the MathML source">E₆,E₇,E₈$E_6,E_7,E_8$, and 1-s2.0-S0021869316302733&_mathId=si8.gif&_user=111111111&_pii=S0021869316302733&_rdoc=1&_issn=00218693&md5=1db3b51313fd9fdc9fda83c31f87e723" title="Click to view the MathML source">F₄$F_4$.