D. W. Thompson and J. Bonner, On Growth and Form, 1992.

X. Pennec and V. Arsigny, Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups, Matrix Information Geometry, pp.123-168, 2012.
DOI : 10.1007/978-3-642-30232-9_7

URL : https://hal.archives-ouvertes.fr/hal-00699361

M. Fréchet, L'intégrale abstraite d'une fonction abstraite d'une variable abstraite et son application a la moyenne d'un élément aléatoire de nature quelconque, 1944.

M. Fréchet, Les éléments aléatoires de nature quelconque dans un espace distancié. Annales de l'institut Henri Poincaré, pp.215-310, 1948.

H. Karcher, Riemannian center of mass and mollifier smoothing, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.509-541, 1977.
DOI : 10.1002/cpa.3160300502

W. S. Kendall, Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence, Proc. Lond, pp.3-61, 1990.
DOI : 10.1112/plms/s3-61.2.371

URL : http://plms.oxfordjournals.org/cgi/content/short/s3-61/2/371

M. Émery and G. Mokobodzki, Sur le barycenter d'une probabilité dans une variété, pp.220-233, 1991.

L. Huiling, Estimation of Riemannian Barycentres, LMS J. Comput. Math, vol.7, pp.193-200, 2004.

L. Yang, Abstract, LMS Journal of Computation and Mathematics, vol.43, pp.461-479, 2010.
DOI : 10.1112/S1461157020090531

URL : https://hal.archives-ouvertes.fr/hal-01153717

B. Afsari, Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity, Proc. Am. Math. Soc. 2011, pp.655-673
DOI : 10.1090/S0002-9939-2010-10541-5

S. Sternberg, Lectures on Differential Geometry, 1964.

E. Cartan, Sur la Structure des Groupes de Transformations Finis et Continus, 1933.

S. T. Tsou, A. G. Walker, and . Xix, XIX.???Metrisable Lie Groups and Algebras, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, vol.64, issue.03, pp.290-304, 1957.
DOI : 10.1017/S0080454100007512

S. T. Tsou and . Xi, XI.???On the Construction of Metrisable Lie Algebras, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, vol.64, issue.02, pp.116-127, 1962.
DOI : 10.1017/S0080454100007755

V. V. Astrakhantsev, Decomposability of metrizable Lie algebras, Functional Analysis and Its Applications, vol.24, issue.3, pp.210-212, 1978.
DOI : 10.1007/BF01681434

V. Keith, On Invariant Bilinear Forms on Finite-dimensional Lie Algebras, 1984.

A. Medina and P. Revoy, Les groupes oscillateurs et leurs reseaux, Manuscripta Mathematica, vol.4, issue.1-3, pp.81-95, 1985.
DOI : 10.1007/BF01171487

URL : http://www.digizeitschriften.de/download/PPN365956996_0052/PPN365956996_0052___log8.pdf

A. K. Guts and A. Levichev, On the Foundations of Relativity Theory, Doklady Akademii Nauk SSSR, vol.277, pp.1299-1303, 1984.

A. Medina, Groupes de Lie munis de pseudo-métriques de Riemann bi-invariantes. Sémin. géométrie différentielle 1981-1982, p.p, 1982.

A. Medina and P. Revoy, Algèbres de Lie et produit scalaire invariant. Annales scientifiques de l'École Normale Supérieure, pp.553-561, 1985.
DOI : 10.24033/asens.1496

K. H. Hofmann and V. S. Keith, Invariant quadratic forms on finite dimensional lie algebras, Bulletin of the Australian Mathematical Society, vol.30, issue.01, pp.21-36, 1986.
DOI : 10.1016/S0001-8708(76)80002-3

M. Bordemann, Nondegenerate invariant bilinear forms on nonassociative algebras, pp.151-201, 1997.

G. Favre and L. Santharoubane, Symmetric, invariant, non-degenerate bilinear form on a Lie algebra, Journal of Algebra, vol.105, issue.2, pp.451-464, 1987.
DOI : 10.1016/0021-8693(87)90209-2

R. Campoamor-stursberg, Quasi-Classical Lie Algebras and their Contractions, International Journal of Theoretical Physics, vol.12, issue.2, pp.583-598, 2008.
DOI : 10.1007/s10773-007-9482-3

URL : http://arxiv.org/abs/hep-th/0610318

S. Benayadi and A. Elduque, Classification of quadratic Lie algebras of low dimension, Journal of Mathematical Physics, vol.55, issue.8, pp.55-081703, 2014.
DOI : 10.1063/1.4890646

URL : https://hal.archives-ouvertes.fr/hal-01101544

J. Hilgert and K. Hofmann, Lorentzian cones in real Lie algebras, Monatshefte f???r Mathematik, vol.14, issue.2, pp.183-210, 1985.
DOI : 10.1007/BF01299267

I. Kath and M. Olbrich, Metric Lie algebras with maximal isotropic centre, Mathematische Zeitschrift, vol.246, issue.1-2, pp.23-53, 2004.
DOI : 10.1007/s00209-003-0575-2

I. Kath and M. Olbrich, Metric Lie algebras and quadratic extensions. Transform. Groups, pp.87-131, 2006.
DOI : 10.1007/s00031-005-1106-5

URL : http://arxiv.org/abs/math/0312243

M. T. Duong, A New Invariant of Quadratic Lie Algebras and Quadratic Lie Superalgebras, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00673991

V. G. Drinfeld, Quantum Groups, pp.798-820, 1987.

A. Belavin and V. Drinfeld, Triangle Equations and Simple Lie Algebras, Math. Phys. Rev, vol.4, 1998.

P. Delorme, Classification des triples de Manin pour les alg??bres de Lie r??ductives complexes, Journal of Algebra, vol.246, issue.1, pp.97-174, 2001.
DOI : 10.1006/jabr.2001.8887

D. Rand, {PASCAL} programs for identification of Lie algebras: Part 1. Radical?A program to calculate the radical and nil radical of parameter-free and parameter-dependent lie algebras, Comput. Phys. Commun, pp.41-105, 1986.

D. Rand, P. Winternitz, and H. Zassenhaus, On the identification of a Lie algebra given by its structure constants. I. Direct decompositions, levi decompositions, and nilradicals, Linear Algebra and its Applications, vol.109, pp.197-246, 1988.
DOI : 10.1016/0024-3795(88)90210-8

A. M. Cohen, W. A. Graaf, and L. Rónyai, Computations in finite-dimensional Lie algebras, Discret. Math. Theor. Comput. Sci, vol.1, pp.129-138, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00955695

L. Ronyai, G. Ivanyos, A. Küronya, and W. A. De-graaf, Computing Levi Decompositions in Lie algebras, Appl. Algebra Eng. Commun. Comput, vol.8, pp.291-303, 1997.

D. Graaf and W. , Lie Algebras: Theory and Algorithms; North-Holland Mathematical Library, 2000.

M. Postnikov and V. Geometry, Riemannian Geometry; Encyclopaedia of Mathematical Sciences, 2001.

N. Bourbaki, Lie Groups and Lie Algebras, pp.1-3, 1989.

J. Milnor, Curvatures of left invariant metrics on lie groups, Advances in Mathematics, vol.21, issue.3, pp.293-329, 1976.
DOI : 10.1016/S0001-8708(76)80002-3

R. H. Bartels and G. W. Stewart, Solution of the matrix equation AX + XB = C [F4], Communications of the ACM, vol.15, issue.9, pp.820-826, 1972.
DOI : 10.1145/361573.361582

J. Grünwald, ??ber duale Zahlen und ihre Anwendung in der Geometrie, Monatshefte f??r Mathematik und Physik, vol.17, issue.1, pp.81-136, 1906.
DOI : 10.1007/BF01697639

E. Levi, Sulla struttura dei gruppi finiti e continui, pp.551-565, 1905.

M. Ceballos, J. Núñez, and A. F. Tenorio, Algorithmic method to obtain abelian subalgebras and ideals in Lie algebras, International Journal of Computer Mathematics, vol.77, issue.35, pp.1388-1411, 2012.
DOI : 10.1063/1.528721

O. Motsak, Computation of the Central Elements and Centralizers of Sets of Elements in Non-Commutative Polynomial Algebras, 2006.

I. Schur, Neue Begründung der Theorie der Gruppencharaktere, pp.406-432, 1905.
DOI : 10.1007/978-3-642-61947-2_7

G. Frobenius, Ueber lineare Substitutionen und bilineare Formen., Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.1878, issue.84, pp.1-63
DOI : 10.1515/crll.1878.84.1

P. A. Brooksbank and E. M. Luks, Testing isomorphism of modules, Journal of Algebra, vol.320, issue.11, pp.4020-4029, 2008.
DOI : 10.1016/j.jalgebra.2008.07.014

A. Karger and N. Josef, Space Kinematics and Lie Groups Translation of: Prostorová kinematika a Liehovy grupy, 1985.

B. Kenwright, A Beginners Guide to Dual-Quaternions: What They Are, How They Work, and How to Use Them for 3D Character Hierarchies, Proceedings of the The 20th International Conference on Computer Graphics, Visualization and Computer Vision, pp.25-28, 2012.