Non-Commutative Resistance Networks
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146653 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Non-Commutative Resistance Networks / M.A. Rieffel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639441606082560 |
|---|---|
| author | Rieffel, M.A. |
| author_facet | Rieffel, M.A. |
| citation_txt | Non-Commutative Resistance Networks / M.A. Rieffel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-01T01:56:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146653 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T01:56:14Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rieffel, M.A. 2019-02-10T15:10:53Z 2019-02-10T15:10:53Z 2014 Non-Commutative Resistance Networks / M.A. Rieffel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L87; 46L57; 58B34 DOI:10.3842/SIGMA.2014.064 https://nasplib.isofts.kiev.ua/handle/123456789/146653 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Commutative Resistance Networks Article published earlier |
| spellingShingle | Non-Commutative Resistance Networks Rieffel, M.A. |
| title | Non-Commutative Resistance Networks |
| title_full | Non-Commutative Resistance Networks |
| title_fullStr | Non-Commutative Resistance Networks |
| title_full_unstemmed | Non-Commutative Resistance Networks |
| title_short | Non-Commutative Resistance Networks |
| title_sort | non-commutative resistance networks |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146653 |
| work_keys_str_mv | AT rieffelma noncommutativeresistancenetworks |