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Pre-symplectic algebroids and their applications
澳门新葡8455最新网站:2016年04月11日 00:00 点击数:

报告人:生云鹤

报告地点:澳门新葡8455最新网站317室

报告澳门新葡8455最新网站:2016年04月18日星期一15:00-16:00

邀请人:

报告摘要:

In this talk, I will introduce the notion of a pre-symplectic algebroid, and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebroids. We study three classes of pre-symplectic algebroids in detail. First we study exact pre-symplectic algebroids and show that they are classified by the third cohomology group of a left-symmetric algebroid. Then we study pre-symplectic algebroids that are direct sums of two transversal Dirac structures, which turn out to be equivalent to left-symmetric bialgebroids. We construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. The Manin triple theory for left-symmetric algebroids is established. Finally, we study para-complex pre-symplectic algebroids. The multiplication in a para-complex pre-symplectic algebroid characterizes the restriction to the Lagrangian subalgebroids of the Levi-Civita connection in the corresponding pseudo-Riemannian Lie algebroid.

主讲人概况:

生云鹤,吉林大学数学新葡京最新官网教授,博士生导师。博士毕业于北京大学数学新葡京最新官网,曾在德国哥廷根大学从事博士后的研究工作,以联合培养博士生的身份在荷兰乌特列支大学学习。多次赴澳大利亚、德国、法国、意大利、荷兰、卢森堡、瑞士等国的高校和科研机构参加学术会议和学术交流。曾受邀在全国代数学大会作大会学术报告。从事数学物理、Poisson几何和高阶结构(李理论)等方向的研究,在CMP、IMRN、J. Algebra等杂志发表SCI检索论文30余篇。

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