Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Spectral Distances: Results for Moyal Plane and Noncommutative Torus
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Spectral Distances: Results for Moyal Plane and Noncommutative Torus
Інший ID:
2010 Mathematics Subject Classification: 58B34; 46L52; 81T75
DOI:10.3842/SIGMA.2010.026
DOI:10.3842/SIGMA.2010.026
Посилання:
Spectral Distances: Results for Moyal Plane and Noncommutative Torus / E. Cagnache, J.C. Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 18–20, 2009, Prague, Czech Republic). The full collection is available at http://www.emis.de/journals/SIGMA/ISQS2009.html.
One of us (E.C.) thanks the organizers of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries for their kind invitation which motivated the present paper. We thank the referees for their fruitful suggestions and comments that helped us to improve the initial version of this paper. Discussions and correspondence on various metric aspects of noncommutative geometry with F. d’Andrea and P. Martinetti are gratefully acknowledged. One of us (JCW) thanks F. Lizzi and B. Iochum for discussions and comments. We thank E. Jolibois for discussions at various stage of this work.
Дата:
2010
Переглядів:
515
Завантажень:
224
Анотація:
The spectral distance for noncommutative Moyal planes is considered in the framework of a non compact spectral triple recently proposed as a possible noncommutative analog of non compact Riemannian spin manifold. An explicit formula for the distance between any two elements of a particular class of pure states can be determined. The corresponding result is discussed. The existence of some pure states at infinite distance signals that the topology of the spectral distance on the space of states is not the weak * topology. The case of the noncommutative torus is also considered and a formula for the spectral distance between some states is also obtained.
