Open this publication in new window or tab >>2022 (English)In: Mathematical physics, analysis and geometry, ISSN 1385-0172, E-ISSN 1572-9656, Vol. 25, no 3, article id 19Article in journal (Refereed) Published
Abstract [en]
We introduce q-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with q-deformed derivations. We show that such connections always exist on projective modules. Furthermore, a condition for metric compatibility is introduced, and an explicit formula is given, parametrizing all metric connections on a free module. On the quantum 3-sphere, a q-deformed torsion freeness condition is introduced and we derive explicit expressions for the Christoffel symbols of a Levi-Civita connection for a general class of metrics. We also give metric connections on a class of projective modules over the quantum 2-sphere. Finally, we outline a generalization to any Hopf algebra with a (left) covariant calculus and associated quantum tangent space.
Place, publisher, year, edition, pages
Springer, 2022
Keywords
Noncommutative geometry; Noncommutative Levi-Civita connection; Quantum groups
National Category
Algebra and Logic
Identifiers
urn:nbn:se:liu:diva-187283 (URN)10.1007/s11040-022-09431-8 (DOI)000821601500002 ()
Note
Funding Agencies|Swedish Research Council [2017-03710]; INFN; Iniziativa Specifica GAST; INDAM-GNSAGA; INDAM-CNRS IRL-LYSM; INFN-Trieste
2022-08-172022-08-172023-05-04