Journal of Lie Theory

no. 3
Metacurvature of Riemannian Poisson-Lie Groups
Amine Bahayou1; Mohamed Boucetta2
1Université Kasdi Merbah, B.P. 511 -- Route de Ghardaia, 30000 Ouargla, Algeria
2Faculté des Sciences et Techniques, BP 549, Guéliz - Marrakech, Morocco
Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 439-462
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.
DOI: 10.5802/jolt.562
Classification: 58B34, 46I65, 53D17
Keywords: Poisson-Lie groups, contravariant connections, metacurvature, spectral triple

Amine Bahayou  1 ; Mohamed Boucetta  2

1 Université Kasdi Merbah, B.P. 511 -- Route de Ghardaia, 30000 Ouargla, Algeria
2 Faculté des Sciences et Techniques, BP 549, Guéliz - Marrakech, Morocco 
Amine Bahayou; Mohamed Boucetta. Metacurvature of Riemannian Poisson-Lie Groups. Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 439-462. doi: 10.5802/jolt.562
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     title = {Metacurvature of {Riemannian} {Poisson-Lie} {Groups}},
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     year = {2009},
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     doi = {10.5802/jolt.562},
     zbl = {1186.58006},
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}
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