非交换电阻网络
Non-Commutative Resistance Networks
摘要：
在有限维$C^*$ -代数${\mathcal A}$的设置中，我们定义了我们称之为${\mathcal A}$的黎曼度量，当${\mathcal A}$是交换的时，它与有限电阻网络非常密切相关。我们探讨了狄利克雷形式和相应的马尔可夫和莱布尼茨，相应的矩阵结构和度量的状态空间上的范数的关系。我们还研究了相关的拉普拉斯和狄拉克算子，商能量范数，电阻距离，以及与标准差的关系。
英文摘要：
In the setting of finite-dimensional $C^*$-algebras ${\mathcal A}$ we define what we call a Riemannian metric for ${\mathcal A}$, which when ${\mathcal A}$ is commutative is very closely related to a finite resistance network. We explore the relationship with Dirichlet forms and corresponding seminorms that are Markov and Leibniz, with corresponding matricial structure and metric on the state space. We also examine associated Laplace and Dirac operators, quotient energy seminorms, resistance distance, and the relationship with standard deviation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
