【讲座题目】Dispersing representations of C*-subalgebras of complex matrices
【主 讲 人】张远航 教授(吉林大学)
【讲座时间】2022年11月18号 周五上午10点-11点
【腾讯会议】ID:823-359-566
【报告人简介】张远航,吉林大学数学学院教授,博士生导师,主要研究兴趣包括:C*-代数分类理论及应用、套代数的可逆元群连通性问题、矩阵代数关于off-diagonal corner的一些问题。已在JFA、JNCG、Studia Math.、PAMS、LAA及中国科学(中、英文版)等杂志上发表(含已接受)学术论文10多篇。现主持国家自然科学基金面上基金一项。
【讲座内容简介】In this talk, we consider the problem of determining the maximum dimension of $P^\perp (\mathcal{A} \oplus \mathcal{B}) P$, where $\mathcal{A}$ and $\mathcal{B}$ are unital, C*-subalgebras of the set $\mathbb{M}_n$ of $n \times n$ complex matrices, and $P \in \mathbb{M}_{2n}$ is a projection of rank $n$. We exhibit a number of equivalent formulations of this problem, including the one which occupies the majority of the talk, namely: determine the minimum dimension of the space $\mathcal{A} \cap S^{-1} \cmathcal{B} S$, where $S$ is allowed to range over the invertible group $\textsc{GL}(n, \mathbb{C})$ of $\mathbb{M}_n$. This problem in turn is seen to be equivalent to the problem of finding two automorphisms $\alpha$ and $\beta$ of $\mathbb{M}_n$ for which the dimension of $\alpha(\mathcal{A}) + \beta(\mathcal{B})$ is maximised. This is a joint work with Laurent Marcoux and Heydar Radjavi.