Differential Geometry
Multiplicative noncommutative deformations of left invariant Riemannian metrics on Heisenberg groups
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 791-796.

Let Hn be the Heisenberg group of dimension 2n+1. We give a precise description of all (π,,), where π is a multiplicative Poisson tensor on Hn and , is a left invariant metric on Hn such that (π,,) satisfies the necessary conditions, introduced by Eli Hawkins, to the existence of a noncommutative deformation of the spectral triple associated to (Hn,,).

Soit Hn le groupe de Heisenberg de dimension 2n+1. Nous donnons une description complète des couples (π,,)π est un tenseur de Poisson multiplicatif et , une métrique invariante à gauche sur Hn tels que (π,,) vérifie les conditions nécessaires, introduites par Eli Hawkins, à l'existence d'une déformation non commutative du triple spectral associé à (Hn,,).

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DOI: 10.1016/j.crma.2009.04.013
Bahayou, Amine 1; Boucetta, Mohamed 2

1 Université Ouargla, BP 511, route Ghardaïa, 30000 Ouargla, Algeria
2 Faculté des sciences et techniques Gueliz, BP 549, 40000 Marrakech, Morocco
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Bahayou, Amine; Boucetta, Mohamed. Multiplicative noncommutative deformations of left invariant Riemannian metrics on Heisenberg groups. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 791-796. doi : 10.1016/j.crma.2009.04.013. http://www.numdam.org/articles/10.1016/j.crma.2009.04.013/

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