We study the triple (G, π, .,.> ) where G is a connected and simply connected Lie group, π and .,.> 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 π) of the spectral triple associated to .,.> are satisfied. We show that the geometric problem of the classification of such triples (G, π, .,.> ) is equivalent to an algebraic one. We solve this algebraic problem in low dimensions and we give a list of all triples (G, π, .,.> ) satisfying Hawkins's conditions, up to dimension four.
@article{JOLT_2009_19_3_a0,
author = {Amine Bahayou and Mohamed Boucetta},
title = {Metacurvature of {Riemannian} {Poisson-Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {439--462},
year = {2009},
volume = {19},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a0/}
}
TY - JOUR
AU - Amine Bahayou
AU - Mohamed Boucetta
TI - Metacurvature of Riemannian Poisson-Lie Groups
JO - Journal of Lie Theory
PY - 2009
SP - 439
EP - 462
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a0/
ID - JOLT_2009_19_3_a0
ER -
%0 Journal Article
%A Amine Bahayou
%A Mohamed Boucetta
%T Metacurvature of Riemannian Poisson-Lie Groups
%J Journal of Lie Theory
%D 2009
%P 439-462
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a0/
%F JOLT_2009_19_3_a0
