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Multiplicative deformations of spectrale triples associated to left invariant metrics on Lie groups
- Publication Year :
- 2009
-
Abstract
- We study the triple $(G,\pi,\prs)$ where $G$ is a connected and simply connected Lie group, $\pi$ and $\prs$ are, respectively, a multiplicative Poisson tensor and a left invariant Riemannian metric on $G$ such that the necessary conditions, introduced by Hawkins, to the existence of a non commutative deformation (in the direction of $\pi$) of the spectrale triple associated to $\prs$ are satisfied. We show that the geometric problem of the classification of such triple $(G,\pi,\prs)$ is equivalent to an algebraic one. We solve this algebraic problem in low dimensions and we give the list of all $(G,\pi,\prs)$ satisfying Hawkins's conditions, up to dimension four.<br />Comment: 23 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0906.2887
- Document Type :
- Working Paper