Infinite Kostant cascades and centrally generated primitive ideals of in types ,

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• 作者：Mikhail V. Ignatyev^a ; ^{mihail.ignatev@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ivan Penkov^b ; ^{i.penkov@jacobs-university.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：17B65 ; 17B35 ; 17B10
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：447
• 期：Complete
• 页码：109-134
• 全文大小：557 K

文摘

We study the center of U(n)$U(\mathfrak{n})$, where n$\mathfrak{n}$ is the locally nilpotent radical of a splitting Borel subalgebra of a simple complex Lie algebra g=sl_∞(C)$\mathfrak{g}={\mathfrak{sl}}_{\infty }(\mathbb{C})$, so_∞(C)${\mathfrak{so}}_{\infty }(\mathbb{C})$, sp_∞(C)${\mathfrak{sp}}_{\infty }(\mathbb{C})$. There are infinitely many isomorphism classes of Lie algebras n$\mathfrak{n}$, and we provide explicit generators of the center of U(n)$U(\mathfrak{n})$ in all cases. We then fix n$\mathfrak{n}$ with “largest possible” center of U(n)$U(\mathfrak{n})$ and characterize the centrally generated primitive ideals of U(n)$U(\mathfrak{n})$ for g=sl_∞(C)$\mathfrak{g}={\mathfrak{sl}}_{\infty }(\mathbb{C})$, sp_∞(C)${\mathfrak{sp}}_{\infty }(\mathbb{C})$ in terms of the above generators. As a preliminary result, we provide a characterization of the centrally generated primitive ideals in the enveloping algebra of the nilradical of a Borel subalgebra of sl_n(C)${\mathfrak{sl}}_n(\mathbb{C})$, sp_2n(C)${\mathfrak{sp}}_{2n}(\mathbb{C})$.