Spectral Distances: Results for Moyal Plane and Noncommutative Torus

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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dc.contributor.author	Cagnache, E.
dc.contributor.author	Wallet, J.C.
dc.date.accessioned	2019-02-08T20:53:46Z
dc.date.available	2019-02-08T20:53:46Z
dc.date.issued	2010
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 58B34; 46L52; 81T75
dc.identifier.other	DOI:10.3842/SIGMA.2010.026
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146321
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Spectral Distances: Results for Moyal Plane and Noncommutative Torus	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA