58
Views
1
CrossRef citations to date
0
Altmetric
Research Articles

Abelian factors in 2-step nilpotent Lie algebras constructed from graphs

, , &
Pages 2155-2175 | Received 29 Aug 2022, Accepted 17 Nov 2022, Published online: 06 Dec 2022

References

  • Alfaro, A., Alvarez, M., Anza, Y. (2022). Degenerations of graph Lie algebras. Linear Multilinear Algebra. 70(1): 91–100. DOI: 10.1080/03081087.2020.1712317.
  • Andrada, A., Dotti, I. (2021). Killing-Yano 2-forms on 2-step nilpotent Lie groups. Geom. Dedicata. 212: 415–424. DOI: 10.1007/s10711-020-00564-0.
  • Bondy, J. A., Murty, U. S. R. (2008). Graph Theory. Berlin: Springer.
  • Chakrabarti, D., Mainkar, M., Swiatlowski, S. (2020). Automorphism groups of nilpotent Lie algebras associated to certain graphs. Commun. Algebra 48(1):263–273. DOI: 10.1080/00927872.2019.1640239.
  • Conti, D., del Barco, V., Rossi, F. (2021). Diagram involutions and homogeneous Ricci-flat metrics. Manuscripta Math. 165(3–4):381–413.
  • Dani, S. G., Mainkar, M. G. (2005). Anosov automorphisms on compact nilmanifolds associated with graphs. Trans. Amer. Math. Soc. 357:2235–2251. DOI: 10.1090/S0002-9947-04-03518-4.
  • DeCoste, R., DeMeyer, L., Mainkar, M. G. (2018). Graphs and metric 2-step nilpotent Lie algebras. Adv. Geom. 18(3):265–284.
  • Deré, J., Mainkar, M. (2021). Anosov diffeomorphisms on infra-nilmanifolds associated to graphs. Math. Nachr. (to appear). https://arxiv.org/pdf/2008.09717.pdf.
  • Eberlein, P. (1994). Geometry of 2-step nilpotent groups with a left invariant metric, I. Ann. Scient. École Normale Sup. (4) 27(5):611–660.
  • Eberlein, P. (1994), Geometry of 2-step nilpotent groups with a left invariant metric II. Trans. Amer. Math. Soc. 343:805–828. DOI: 10.2307/2154743.
  • Erdős, P. (1977). On the chromatic index of almost all graphs. J. Combin. Theory Ser. B. 23:225–257.
  • Fanaї, H. (2007). Einstein solvmanifolds and graphs. C. R. Math. 344(1):37–39.
  • Farinati, M., Jancsa, A. (2018). Lie bialgebra structures on 2-step nilpotent graph algebras. J. Algebra. 505:70–91. DOI: 10.1016/j.jalgebra.2018.03.003.
  • Gornet, R., Mast, M. (2000). The length spectrum of Riemannian two-step nilmanifolds. Ann. Scient. École Normale Sup. (4) 33(2):181–209.
  • Grantcharov, G., Grantcharov, V., Iliev, P. (2017). Solvable Lie algebras and graphs. J. Algebra. 491:474–489. DOI: 10.1016/j.jalgebra.2017.08.015.
  • Gross, J. L. (1977). Every connected regular graph of even degree is a Schreier coset graph. J. Comb. Theory. 22: 227–232. DOI: 10.1016/0095-8956(77)90068-5.
  • Kaplan, A. (1981). Riemannian nilmanifolds attached to Clifford modules. Geom. Dedicata. 11:127–136. DOI: 10.1007/BF00147615.
  • Kaplan, A. (1983). On the geometry of groups of Heisenberg type. Bull. London Math. Soc. 15(1):35–42.
  • Lauret, J., Will, C. (2008). On Anosov automorphisms of nilmanifolds. J. Pure Appl. Algebra. 212(7):1747–1755.
  • Lauret, J., Will, C. (2011). Einstein solvmanifolds: Existence and non-existence questions. Math. Ann. 350(1): 199–225.
  • Lee, K., Park, K. (1996). Smoothly closed geodesics in 2-step nilmanifolds. Indiana Univ. Math. J. 45:1–14. DOI: 10.1512/iumj.1996.45.1077.
  • Mainkar, M. (2015). Graphs and two-Step nilpotent Lie algebras. Groups Geom. Dyn. 9(1):55–65.
  • Nikolayevsky, Y. (2020). Geodesic orbit and naturally reductive nilmanifolds associated with graphs. Math. Nachr. 293(4):754–760.
  • Ovando, G. (2020). The geodesic flow on nilmanifolds associated to graphs. Rev. Un. Mat. Argentina. 61(2): 315–338. DOI: 10.33044/revuma.v61n2a09.
  • Payne, T. L., Schroeder, M. (2017). Uniform Lie algebras and uniformly colored graphs. Adv. Geom. 17(4):507–524.
  • Pouseele, H., Tirao, P. (2009). Compact symplectic nilmanifolds associated with graphs. J. Pure Appl. Algebra. 213(9):1788–1794.
  • Ray, A. (2016). Two-step and three-step nilpotent Lie algebras constructed from Schreier graphs. J. Lie Theory. 26(2):479–495.

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.