简单结构图上的代数

M. Belishev, A. Kaplun
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引用次数: 3

摘要

一个对偶代数${\mathfrak E}(\Omega)$是一个与度量图$\Omega$相关的C*代数。它由与图相关联的动力系统的轨迹和可达集决定。该系统描述了由边界源(控制)发起并以有限速度传播到图形中的波。对偶代数的动机和兴趣来自于通过其动态和/或谱边界数据重构图的逆问题。代数${\mathfrak E}(\Omega)$是由这些数据决定的。同时,它的结构和代数不变量(不可约表示)与$\Omega$的拓扑相联系。我们以一个简单结构的$\Omega$为例,证明了这种联系并研究了${\mathfrak E}(\Omega)$。希望在未来,这些联系将为重建提供一种方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Eikonal algebra on a graph of simple structure
An eikonal algebra ${\mathfrak E}(\Omega)$ is a C*-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are initiated by boundary sources (controls) and propagate into the graph with finite velocity. Motivation and interest to eikonal algebras comes from the inverse problem of reconstruction of the graph via its dynamical and/or spectral boundary data. Algebra ${\mathfrak E}(\Omega)$ is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of $\Omega$. We demonstrate such connections and study ${\mathfrak E}(\Omega)$ by the example of $\Omega$ of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.
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