Solvable Lie algebras, products by generators, and some of its applications
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 85-94.

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In this work, we enlarge the definition of products by generators of Lie algebras to the class of solvable Lie algebras. We analyze the number of independent invariant functions for the coadjoint representation of these algebras by means of the Maurer–Cartan equations and give some applications to product structures on Lie algebras.
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R. Campoamor-Stursberg. Solvable Lie algebras, products by generators, and some of its applications. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 85-94. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a6/

[1] Berzin D. V., “Invarianty koprisoedinënnogo predstavleniya dlya algebr Li nekotorogo spetsialnogo vida”, Uspekhi mat. nauk, 51:1 (1996), 141–143 | MR

[2] Mubarakzyanov G. M., “O razreshimykh algebrakh Li”, Izv. vyssh. uchebn. zaved. Matematika, 1963, no. 1, 114–123 | MR | Zbl

[3] Perelomov A. M., Integriruemye sistemy klassicheskoi mekhaniki i algebry Li, RKhD, M., 2002

[4] Trofimov V. V., Vvedenie v geometriyu mnogoobrazii s simmetriyami, Izd-vo Mosk. un-ta, M., 1989 | MR

[5] Ancochea J. M., Campoamor-Stursberg R., “Symplectic forms and products by generators”, Comm. Algebra, 30 (2002), 4235–4249 | DOI | MR | Zbl

[6] Ancochea J. M., Campoamor-Stursberg R., “Two step solvable Lie algebras and weight graphs”, Transform. Groups, 7 (2002), 307–320 | DOI | MR | Zbl

[7] Ancochea J. M., Campoamor-Stursberg R., “Characteristically nilpotent Lie algebras of type $\mathfrak{g}_{1}\underline{\times}\mathfrak{g}_{2}$”, Forum Math., 15 (2003), 299–307 | DOI | MR | Zbl

[8] Andrada A., Barberis M. L., Dotti I., Ovando G., Product structures on four dimensional solvable Lie algebras, , 2004 arXiv: /math.RA/0402234 | MR

[9] Campoamor-Stursberg R., “A graph theoretical determination of solvable complete rigid Lie algebras”, Linear Algebra Appl., 372 (2003), 53–66 | DOI | MR | Zbl

[10] Campoamor-Stursberg R., “An alternative interpretation of the Beltrametti–Blasi formula by means of differential forms”, Phys. Lett. A, 327 (2004), 138–145 | DOI | MR | Zbl

[11] Turkowski P., “Solvable Lie algebras of dimension six”, J. Math. Phys., 31 (1990), 1344–1350 | DOI | MR | Zbl