Partial classification of cuspidal simple modules for Virasoro-like algebra

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• 作者：Jian-Jian Jiang^a ; ^{j.j.jiang@foxmail.com" class="auth_mail" title="E-mail the corresponding author} ; Wei-Qiang Lin^b
• 关键词：17B10 ; 17B63 ; 17B65 ; 17B66 ; 17B68 ; 17B70
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：464
• 期：Complete
• 页码：266-278
• 全文大小：312 K

文摘

Let P$\mathfrak{P}$ be the Lie algebra of Hamiltonian vector fields on the torus, which is also known as the Virasoro-like algebra, a special kind of the so-called Block type Lie algebra. And let A$\mathfrak{A}$ be the Laurent polynomial algebra in two variables. In this paper, by following S.E. Rao's strategy of “backward induction”, we prove that any quasi-finite simple (A,P)$(\mathfrak{A},\mathfrak{P})$-module has to come from Larsson–Shen's construction.