题  目: Derived noncommutative Poisson structures and their applications

报告人: 陈小俊教授   四川大学数学学院

时  间: 11月11日 星期一 下午2:00 - 3:30

地  点: 管理科研楼1611会议室

摘 要:  Recently, Crawley-Boevey introduced a notion of noncommutative Poisson structure for an associative algebra $A$ (viewed as a noncommutative space). It has a very good property that it naturally induces a Poisson structure on the moduli space of representations of $A$. Crawley-Boevey called such noncommutative Poisson structure an $H_0$-Poisson structure. In this talk we generalize Crawley-Boevey's result to all higher degrees. It is represented by a Lie bracket on the cyclic homology $/mathrm{HC}_/bullet(A)$ of $A$, which then induces a (graded) commutative Poisson structure on the derived moduli space of representations of $A$. After that, we give several interesting examples and applications in/to algebra and geometry, such as Calabi-Yau algebras and Fukaya category. Joint work with Berest, Eshmatov and Ramadoss.

研究生教育创新计划GAP研讨班简介: 本系列研讨班旨在介绍一些当前极其活跃的数学研究课题和领域，扩充大家的视野，在一定程度上填补研究生数学和研究数学之间的GAP。报告者将尽可能地介绍该课题的背景，概念，已有结果及主要问题。本系列报告的范围将涉及几何(G)，代数，分析(A)以及数学物理(P)等各方面。

GAP研讨班主页: http://staff.ustc.edu.cn/~wangzuoq/GAP/gap13F.html

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