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Jet modules for the vector field Lie algebras
时间:2021年07月28日 10:45 点击数:

报告人:刘根强

报告地点:澳门永利唯一网址104教室

报告时间:2021年07月29日星期四10:00-11:00

邀请人:谭海军

报告摘要:

For a commutative algebra $A$ over $\mathbb{C}$, let $\mathfrak{g}=\text{Der}(A)$. A module over  the smash product $A\# U(\mathfrak{g})$ is called a jet $\mathfrak{g}$-module, where $U(\mathfrak{g})$ is the universal enveloping algebra of $\mathfrak{g}$. In this talk, we talk about jet modules when $A=\mathbb{C}[t_1^{\pm 1},t_2]$. We show that  $A\#U(\mathfrak{g})\cong\mathcal{D}\otimes U(L)$, where $\mathcal{D}$ is the Weyl   algebra $\mathbb{C}[t_1^{\pm 1},t_2, \frac{\partial}{\partial t_1},\frac{\partial}{\partial t_2}]$, and $L$ is a Lie subalgebra of  $A\# U(\mathfrak{g})$ called the jet Lie algebra corresponding to $\mathfrak{g}$. Using a Lie algebra isomorphism $\theta:L \rightarrow \mathfrak{m}_{1,0}\Delta$,  where $\mathfrak{m}_{1,0}\Delta$ is the subalgebra of vector fields vanishing at the point $(1,0)$, we show that any irreducible finite dimensional  $L$-module is isomorphic to an irreducible $\gl_2$-module. As an application, we  give  tensor product realizations of  irreducible   jet modules over $\mathfrak{g}$ with uniformly bounded weight spaces。


主讲人简介:

刘根强,河南大学澳门永利唯一网址副教授,研究方向为李代数及其表示理论,在Israel J. Math., Bull. Lond. Math. Soc., J. Algebra等杂志发表高水平论文十余篇,主持国家自然科学基金项目两项,并多次在全国性代数及李代数会议上作报告。

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