Journal of Lie Theory

no. 3
Metacurvature of Riemannian Poisson-Lie Groups
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 
@article{JOLT_2009_19_3_a0,
     author = {A. Bahayou and M. Boucetta},
     title = {Metacurvature of {Riemannian} {Poisson-Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {439--462},
     year = {2009},
     volume = {19},
     number = {3},
     doi = {10.5802/jolt.562},
     zbl = {1186.58006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.562/}
}
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A. Bahayou; M. 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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