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Non-Commutative Resistance Networks
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Non-Commutative Resistance Networks
Інший ID:
2010 Mathematics Subject Classification: 46L87; 46L57; 58B34
DOI:10.3842/SIGMA.2014.064
DOI:10.3842/SIGMA.2014.064
Посилання:
Non-Commutative Resistance Networks / M.A. Rieffel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
The research reported here was supported in part by National Science Foundation grant DMS1066368.
Дата:
2014
Переглядів:
537
Завантажень:
257
Анотація:
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.
