59
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Double extensions of left-symmetric structures

Pages 4180-4188 | Received 16 Jan 2024, Accepted 08 Apr 2024, Published online: 26 Apr 2024

References

  • Benoist, Y. (1955). Une nilvariété non affine. J. Differ. Geom. 41(1):21–52.
  • Bourkadi, S., Mansouri, M. (2022). On cosymplectic Lie Algebras. arXiv preprint, arXiv:2204.01569.
  • Burde, D. (1996). Affine structures on nilmanifolds. Int. J. Math. 7(5):599–616. DOI: 10.1142/S0129167X96000323.
  • Burde, D. (1999). Left-invariant affine structures on nilpotent Lie groups. Habilitationsschrift, Düsseldorf.
  • Burde, D., Grunewald, F. (1995). Modules for certain Lie algebras of maximal class. J. Pure Appl. Algebra 99(3):239–254. DOI: 10.1016/0022-4049(94)00002-Z.
  • Campoamor-Stursberg, R. (2009). Symplectic forms on six-dimensional real solvable Lie algebras. I. Algebra Colloq. 16:253–266. DOI: 10.1142/S100538670900025X.
  • Chu, B. Y. (1974). Symplectic homogeneous spaces. Trans. Amer. Math. Soc. 197:145–159. DOI: 10.2307/1996932.
  • Dardié, J. M., Medina, A. (1996). Double extension symplectique d’un group de Lie symplectique. Adv. Math. 117(2):208–227. DOI: 10.1006/aima.1996.0009.
  • Dekimpe, K., Ongenae, V. (2000). On the number of abelian left symmetric algebras. Proc. Amer. Math. Soc. 128(11):3191–3200. DOI: 10.1090/S0002-9939-00-05484-8.
  • Goze, M., Remm, E. (2003). Affine structures on abelian Lie groups. Linear Algebra Appl. 360:215–230. DOI: 10.1016/S0024-3795(02)00452-4.
  • Goze, M., Remm, E. (2000). Non complete affine connections on filiform Lie algebras. arXiv preprint, arXiv:math0007067.
  • Helmstetter, J. (1979). Radical d’une algèbre symétrique a gauche. Ann. Inst. Fourier 29(4):17–35. DOI: 10.5802/aif.764.
  • Humphreys, J. E. (1980). Introduction to Lie Algebras and Representation Theory. New York: Springer-Verlag.
  • Kim, H. (1986). Complete left-invariant affine structures on nilpotent Lie groups. J. Differ. Geom. 24:373–394.
  • Medina, A., Revoy, P. (1985). Algèbres de Lie et produit scalaire invariant. Ann. Sci. Éc. Norm. Supér. (4) 18:553–561. DOI: 10.24033/asens.1496.
  • Medina, A., Revoy, P. (1991). Groupes de Lie à structure symplectique invariante. In: Dazord, P., Weinstein, A., eds. Symplectic Geometry, Groupoids and Integrable Systems. New York: Springer-Verlag, pp. 247–266.
  • Michel, G., Abdelkader, B. (1987). Sur les algèbres de Lie munies d’une forme symplectique. Rend. Sem. Fac. Sci. Univ. Cagliari 57(1):85–97.
  • Milnor, J. (1977). On fundamental groups of complete affinely flat manifolds. Adv. Math. 25:178–187. DOI: 10.1016/0001-8708(77)90004-4.
  • Castellanos, L., Tamaru, H. (2023). A classification of left-invariant symplectic structures on some Lie groups. Beitr. Algebra Geom. 64(2):471–491. DOI: 10.1007/s13366-022-00643-1.
  • Nagano, T., Yagi, K. (1974). The affine structures on the real two-torus. I. Osaka J. Math. 11:181–210.
  • Nijenhuis, A. (1968). Sur une classe de propriétés communes á quelques types différents d’algèbres. Enseign. Math. II. Sér. 14:225–277.
  • Ovando, G. (2006). Four dimensional symplectic Lie algebras. Beitr. Algebra Geom. 47(2):419–434.
  • Segal, D. (1992). The structure of complete left-symmetric algebras. Math. Ann. 293(3):569–578. DOI: 10.1007/BF01444735.
  • Valencia, F. (2021). Flat affine symplectic lie groups. J. Lie Theory 31(1):063–092.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.