Non-Commutative Resistance Networks

作者：Rieffel Marc A^*

来源：Symmetry Integrability and Geometry-Methods and Applications, 2014, 10: 064.

DOI：10.3842/SIGMA.2014.064

• resistance network
• Riemannian metric
• Dirichlet form
• Markov
• Leibniz seminorm
• Laplace operator
• resistance distance
• standard deviation

In the setting of finite-dimensional C*-algebras A we define what we call a Riemannian metric for A, which when 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.

• 出版日期2014