Non-Commutative Resistance Networks

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2014
• 1. Verfasser: Rieffel, M.A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2014
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/146653
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Non-Commutative Resistance Networks / M.A. Rieffel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ.

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 corr...