Levi-Civita's Theorem for Noncommutative Tori

Домашня сторінка
→
Фізико-технічні та математичні науки
→
Відділення математики
→
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
→
Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
→
Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9, випуск за цей рік
→
Переглянути статтю

dc.contributor.author	Rosenberg, J.
dc.date.accessioned	2019-02-21T07:21:13Z
dc.date.available	2019-02-21T07:21:13Z
dc.date.issued	2013
dc.identifier.citation	Levi-Civita's Theorem for Noncommutative Tori / L. Rosenberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 46L87; 58B34; 46L08; 46L08
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2013.071
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149363
dc.description.abstract	We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas.	uk_UA
dc.description.sponsorship	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. This research was supported by NSF grant DMS-1206159. The author thanks the referees and the participants at the Fields Institute Focus Program for several interesting comments and discussions. I would like to thank Joakim Arnlind for pointing out a mistake in the original formulation of Proposition 3.4	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	Levi-Civita's Theorem for Noncommutative Tori	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA