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...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146653 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| id |
irk-123456789-146653 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1466532019-02-11T01:24:30Z Non-Commutative Resistance Networks Rieffel, M.A. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146653 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Rieffel, M.A. |
| spellingShingle |
Rieffel, M.A. Non-Commutative Resistance Networks Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Rieffel, M.A. |
| author_sort |
Rieffel, M.A. |
| title |
Non-Commutative Resistance Networks |
| title_short |
Non-Commutative Resistance Networks |
| title_full |
Non-Commutative Resistance Networks |
| title_fullStr |
Non-Commutative Resistance Networks |
| title_full_unstemmed |
Non-Commutative Resistance Networks |
| title_sort |
non-commutative resistance networks |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146653 |
| citation_txt |
Non-Commutative Resistance Networks / M.A. Rieffel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT rieffelma noncommutativeresistancenetworks |
| first_indexed |
2023-05-20T17:25:21Z |
| last_indexed |
2023-05-20T17:25:21Z |
| _version_ |
1796153258516938752 |