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Curvature and geometric modules of noncommutative spheres and tori
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-8727-2169
2014 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 4, 041705- p.Article in journal (Refereed) Published
Abstract [en]

When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is the projection operator, projecting tangent vectors in the ambient space onto the tangent space of the submanifold. In this note, we point out that there exist noncommutative analogues of these projection operators, which implies a very natural definition of noncommutative tangent spaces as particular projective modules. These modules carry an induced connection from Euclidean space, and we compute its scalar curvature.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2014. Vol. 55, no 4, 041705- p.
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-107859DOI: 10.1063/1.4871175ISI: 000336084100007OAI: diva2:727658
Available from: 2014-06-23 Created: 2014-06-23 Last updated: 2014-08-13Bibliographically approved

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Arnlind, Joakim
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Mathematics and Applied MathematicsThe Institute of Technology
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