2019代数学系列讲座之五(王顶国教授)

发布时间:2019-04-25作者:访问量:10

报告题目PBW-deformations of type $\mathbb{A}_n$ quantum

groups via multiple Ore extensions

报 告 人:王顶国 教授(曲阜师范大学)

报告时间2019429日(周一)下午15:00-16:00

报告地点:磬苑校区数学楼H306报告厅

报告摘要The notion of multiple Ore extension is introduced as a natural generalization of Ore extensions and double Ore extensions.  For a PBW-deformation $\mathcal{B}_q(\mathfrak{sl}(n+1, \mathbb{C}))$  of type $\mathbb {A}_n$ quantum group, we explicitly obtain the commutation relations of its root vectors,  then show that it can be realized via a series of multiple Ore extensions, which we call a ladder Ore extension of type $(1, 2, \cdots, n)$.  Moreover, we analyze the quantum algebras $\mathcal{B}_q(\mathfrak{g})$ of type $\mathbb {D}_4$, $\mathbb{B}_2$ and $\mathbb{G}_2$ and give some examples and counterexamples that can be realized by a ladder Ore extension. This is based on a joint work with Yongjun Xu and Hualin Huang.

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                                         科学技术处

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