97
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Left-symmetric algebra structures on contact Lie algebras

ORCID Icon & ORCID Icon
Pages 2914-2929 | Received 20 May 2022, Accepted 13 Jan 2023, Published online: 06 Feb 2023

References

  • Barajas, T., Roque, E., Salgado, G. (2019). Principal derivations and codimension one ideals on contact and Frobenius Lie algebras. Commun. Algebra 47(12):5380–5391. DOI: 10.1080/00927872.2019.1623238.
  • Burde, D. (1994). Left-symmetric structures on simple modular Lie algebras. J. Algebra 169(1):112–138. DOI: 10.1006/jabr.1994.1275.
  • Burde, D. (1998). Simple left-symmetric algebras with solvable Lie algebra. Manuscripta Math. 95:397–411. DOI: 10.1007/BF02678039.
  • Burde, D. (1999). Left-invariant affine structures on nilpotent Lie groups. Habilitation, Düsseldorf, 1–83.
  • Diatta, A. (2008). Left invariants contact structures on Lie groups. Differ. Geom. Appl. 26(5):544–552. DOI: 10.1016/j.difgeo.2008.04.001.
  • Diatta, A., Manga, B., (2014). On properties of principal elements of Frobenius Lie algebras. J. Lie Theory 24(3): 849–864.
  • Èlashvili, A. G. (1982). Frobenius Lie Algebras. (Russian). Funktsional. Anal. i Prilozhen. 16(4):94–95. DOI: 10.1007/BF01077870.
  • Goze, M., Remm, E. (2014). Contact and Frobeniusian forms on Lie gropus. Differ. Geom. Appl. 35:74–94. DOI: 10.1016/j.difgeo.2014.05.008.
  • Helmstetter, J. (1979). Radical d’une algèbre symétrique a gauche. Ann. Inst. Fourier 29:17–35. DOI: 10.5802/aif.764.
  • Khakimdjanov, Goze, M., Medina, A. (2004). Symplectic or contact structures on Lie gropus. Differ. Geom. Appl. 21:41–54. DOI: 10.1016/j.difgeo.2003.12.006.
  • Milnor, J. (1977). On fundamentals groups of complete affinely flat manifolds. Adv. Math. 25:178–187. DOI: 10.1016/0001-8708(77)90004-4.
  • Mizuhara, A. (1982). On the radical of a left-symmetric algebra. Tensor N. S. 36:300–302.
  • Ooms, A. I. (1980). On Frobenius Lie algebras. Commun. Algebra 8:13–52. DOI: 10.1080/00927878008822445.
  • Remm, E. (2003). Affine structures on nilpotent contact Lie algebras. Arxiv: 0109077v3
  • Segal, D. (1992). The structure of complete left-symmetric algebras. Math. Ann. 293:569–578. DOI: 10.1007/BF01444735.
  • Vinberg, E. B. (1963). Convex homogeneous cones. Transl. Moscow Math. Soc. 12:340–403.

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.