Lie algebras associated with labeled directed graphs

References

• Agrachev, A., Barilari, D., Boscain, U. (2020). A Comprehensive Introduction to Sub-Riemannian Geometry. From the Hamiltonian Viewpoint. With an Appendix by Igor Zelenko. Cambridge Studies in Advanced Mathematics, 181. Cambridge: Cambridge University Press.
   Google Scholar
• Alfaro Arancibia, B., Alvarez, M. A., Anza, Y. (2022). Degenerations of graph Lie algebras. Linear Multilinear Algebra 70(1):91–100. DOI: 10.1080/03081087.2020.1712317.
   Web of Science ®Google Scholar
• Bauer, W., Furutani, K., Iwasaki, C., Laaroussi, A. (2021). Spectral theory of a class of nilmanifolds attached to Clifford modules. Math. Z. 297:557–583. DOI: 10.1007/s00209-020-02525-5.
   Web of Science ®Google Scholar
• Bonfiglioli, A., Lanconelli, E., Uguzzoni, F. (2007). Stratified Lie Groups and Potential Theory for their Sub-Laplacians. Springer Monographs in Mathematics. Berlin: Springer.
   Google Scholar
• Čap, A., Slovak, J. (2009). Parabolic Geometries. I. Background and General Theory. Mathematical Surveys and Monographs, 154. Providence, RI: American Mathematical Society.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Chung, F. (1997). Spectral Graph Theory. Providence, RI: American Mathematical Society.
   Google Scholar
• Corwin, L. J., Greenleaf, F. P. (1990). Representations of Nilpotent Lie Groups and their Applications. Part I. Cambridge Studies in Advanced Mathematics, 18. Cambridge: Cambridge University Press.
   Google Scholar
• Crandall, G., Dodziuk, J. (2002). Integral structures on H-type Lie algebras. J. Lie Theory 12(1):69–79.
   Web of Science ®Google Scholar
• Dani, S. G., Mainkar, M. G. (2005). Anosov automorphisms on compact nilmanifolds associated with graphs. Trans. Amer. Math. Soc. 357(6):2235–2251. DOI: 10.1090/S0002-9947-04-03518-4.
   Web of Science ®Google Scholar
• DeCoste, R., DeMeyer, L., Mainkar, M., Ray, A. (2023). Abelian factors in 2-step nilpotent Lie algebras constructed from graphs. Commun. Algebra 51(5):2155–2175. DOI: 10.1080/00927872.2022.2151612.
   Web of Science ®Google Scholar
• Eberlein, P. (1994). Geometry of 2-step nilpotent groups with a left invariant metric. Ann. Sci. École Norm. Sup. (4) 27(5):611–660. DOI: 10.24033/asens.1702.
   Web of Science ®Google Scholar
• Eberlein, P. (1994). Geometry of 2-step nilpotent groups with a left invariant metric. II. Trans. Amer. Math. Soc. 343(2):805–828. DOI: 10.1090/S0002-9947-1994-1250818-2.
   Web of Science ®Google Scholar
• Furutani, K., Godoy Molina, M., Markina, I., Morimoto, T., Vasilev, A. (2018). Lie algebras attached to Clifford modules and simple graded Lie algebras. J. Lie Theory 28(3):843–864.
   Web of Science ®Google Scholar
• Furutani, K., Markina, I. (2017). Complete classification of pseudo H-type Lie algebras: I. Geom. Dedicata 190:23–51. DOI: 10.1007/s10711-017-0225-1.
   Web of Science ®Google Scholar
• Jurdjevic, V. (1997). Geometric Control Theory. Cambridge Studies in Advanced Mathematics, 52. Cambridge: Cambridge University Press.
   Google Scholar
• Kaplan, A. (1980). Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms. Trans. Amer. Math. 258(1):147–153. DOI: 10.1090/S0002-9947-1980-0554324-X.
   Web of Science ®Google Scholar
• Kaplan, A. (1981). Riemannian nilmanifolds attached to Clifford modules. Geom. Dedicata 11(2):127–136. DOI: 10.1007/BF00147615.
   Google Scholar
• Kushner, A., Lychagin, V., Rubtsov, V. (2007). Contact Geometry and Non-linear Differential Equations. Encyclopedia of Mathematics and its Applications, 101. Cambridge: Cambridge University Press.
   Google Scholar
• Magnin, L. (1986). Sur les algèbres de Lie nilpotentes de dimension ≤7. J. Geom. Phys. 3(1):119–144.
   Google Scholar
• Malcev, A. I. (1951). On a class of homogeneous spaces. Amer. Math. Soc. Translation 39.
   Google Scholar
• Montgomery, R. (2002). A Tour of Subriemannian Geometries, their Geodesics and Applications. Mathematical Surveys and Monographs, 91. Providence, RI: American Mathematical Society.
   Google Scholar
• Nica, B. (2018). A Brief Introduction to Spectral Graph Theory. EMS Textbooks in Mathematics. Zürich: EMS Press.
   Google Scholar
• Nicolussi, S., Ottazzi, A. Polarised Lie groups contactomorphic to stratified groups. arXiv:1807.03854.
   Google Scholar
• Reutenauer, C. (2003). Free Lie Algebras. Handbook of Algebra, Vol. 3. Amsterdam: Elsevier/North-Holland, pp. 887–903.
   Google Scholar
• Ray, A. (2016). Two-step and three-step nilpotent Lie algebras constructed from Schreier graphs. J. Pure Appl. Algebra 28(2):479–495.
   Google Scholar
• Scheuneman, J. (1967). Two-step nilpotent Lie algebras. J. Algebra 7:152–159. DOI: 10.1016/0021-8693(67)90052-X.
   Web of Science ®Google Scholar
• Tanaka, N. (1970). On differential systems, graded Lie algebras and pseudogroups. J. Math. Kyoto Univ. 10:1–82.
   Google Scholar
• Warhurst, B. (2007). Tanaka prolongation of free Lie algebras. Geom. Dedicata 130:59–69. DOI: 10.1007/s10711-007-9205-1.
   Web of Science ®Google Scholar