26
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Geometric Structures On 3-Dimensional Hom-Lie Algebras

, &
Pages 137-175 | Received 01 Mar 2022, Accepted 03 May 2022, Published online: 13 Nov 2022

References

  • M. A. Alvarez, M. C. Rodriguez-vallarte and G. Salgado, Contact nilpotent Lie algebras, Proceedings of the American Mathematical Society, 145, 1467-1474 (2017). doi: 10.1090/proc/13341
  • A. Andrada, A. Fino and L. Vezzoni, A class of Sasakian 5-Manifolds, Transformation Groups, 14, 493-512 (2009). doi: 10.1007/s00031-009-9058-9
  • A. Armakan and M. R. Farhangdoost, Geometric aspects of extensions of hom-Lie superalgebras, International Journal of Geometric Methods in Modern Physics, 14, 1750085 (2017).
  • D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc, Boston (2002).
  • G. Calvaruso and A. Fino, Five-dimensional K-contact Lie algebras, Monatshefte für Mathematik 167, 35-59 (2012). doi: 10.1007/s00605-011-0308-2
  • G. Calvaruso and A. Perrone, Cosymplectic and α-cosymplectic Lie algebras, Complex Manifolds, 3, 252-270 (2016). doi: 10.1515/coma-2016-0013
  • D. Chinea and C. Gonzales, A classification of almost contact metric manifolds, Annali di Matematica Pura ed Applicata. Series IV. 156, 15-36 (1990). doi: 10.1007/BF01766972
  • J. Dixmier, Sur les reprEsentations unitaires des groupes de Lie nilpotentes III, Canadian Journal of Mathematics, 10, 321-348 (1958). doi: 10.4153/CJM-1958-033-5
  • G. Graziani, A. Makhlouf, C. Menini and F. Panaite, BiHom-associative algebras, biHom-Lie algebras and biHom-bialgebras, Sigma Series in Pure Mathematics, 11, 86-120 (2015).
  • B. Guan, L. Chen and B. Sun, On Hom-Lie Superalgebras, Advances in Applied Clifford Algebras, 29(16) (2019).
  • J. Hartwig, D. Larsson, and S. Silvestrov, Deformations of Lie algebras using σ-derivations, Journal of Algebra, 295, 314-361 (2006). doi: 10.1016/j.jalgebra.2005.07.036
  • Y. Khakimdjanov, M. Gozea and A. Medinab, Symplectic or contact structures on Lie groups, Differential Geometry and its Applications, 21, 41-54 (2004). doi: 10.1016/j.difgeo.2003.12.006
  • A. Kitouni, A. Makhlouf and S. Silvestrov, On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras, Georgian Mathematical Journal, 23, 75-95 (2016). doi: 10.1515/gmj-2015-0063
  • J. M. Lee, Introduction to Smooth Manifolds, Springer, 2003.
  • A. Makhlouf and S. Silvestov, Hom-Lie admissible, Hom-coalgebras and Hom-Hopf algebras, Generalized Lie Theory in Mathematics, Physics and Beyond, 189-206 (2008).
  • A. Makhlouf and S. Silvestov, Hom-algebras and Hom-coalgebras, Journal of Algebra and its Applications, 9, 553-589 (2010).
  • A. Makhlouf and S. Silvestov, Hom-algebra structures, Journal of Generalized Lie Theory and Applications, 2, 51-64 (2008).
  • N. Ozdemir, M. Solgun and S. Aktay, Almost contact metric structures on 5-dimensional nilpotent Lie algebra, Symmetry, 8, 1-13 (2016). doi: 10.3390/sym8080076
  • S. Merati, M. R. Farhangdoost and A. Attari Polesangi, Representation up to Homotopy and Hom-Lie Algebroid Modules, Journal of Dynamical Systems and Geometric Theories, 18, 27-37 (2020). doi: 10.1080/1726037X.2020.1788817
  • S. Wang and S. Wang, Hom-Lie algebras in Yetter-Drinfeld categories, Communications in Algebra, 42, 4540-4561 (2014).
  • K. Yano and M. Kon, Structure on Manifold, World Scientific, Singapore, 1984.
  • D. Yau, Hom-bialgebras and comodule algebras, International Electronic Journal of Algebra, 8, 45-64, (2010).
  • D. Yau, The Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi triangular bialgebras, Journal of Physics A: Math Theory, 42, 165-202 (2009). doi: 10.1088/1751-8113/42/16/165202

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.