Geodesic
Universal equivalence of partially commutative Lie algebras
Algebra i logika, Tome 56 (2017) no. 2, pp. 202-225.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study universal theories of partially commutative Lie algebras whose defining graphs are cycles and trees. Within each of the two above-mentioned classes of partially commutative Lie algebras, necessary and sufficient conditions for the coincidence of universal theories are specified.
Keywords: partially commutative Lie algebra, defining graph, universal theory. 
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E. N. Poroshenko. Universal equivalence of partially commutative Lie algebras. Algebra i logika, Tome 56 (2017) no. 2, pp. 202-225. http://geodesic.mathdoc.fr/item/AL_2017_56_2_a4/

[1] G. Duchamp, D. Krob, “Free partially commutative structures”, J. Algebra, 156:2 (1993), 318–361 | DOI | MR | Zbl

[2] H. Servatius, “Automorphisms of graph groups”, J. Algebra, 126:1 (1989), 34–60 | DOI | MR | Zbl

[3] G. Duchamp, D. Krob, “The lower central series of the free partially commutative group”, Semigroup Forum, 45:3 (1992), 385–394 | DOI | MR | Zbl

[4] A. J. Duncan, I. V. Kazachkov, V. N. Remeslennikov, “Parabolic and quasiparabolic subgroups of free partially commutative groups”, J. Algebra, 318:2 (2007), 918–932 | DOI | MR | Zbl

[5] Ch. K. Gupta, E. I. Timoshenko, “Chastichno kommutativnye metabelevy gruppy: tsentralizatory i elementarnaya ekvivalentnost”, Algebra i logika, 48:3 (2009), 309–341 | MR | Zbl

[6] E. I. Timoshenko, “Universalnaya ekvivalentnost chastichno kommutativnykh metabelevykh grupp”, Algebra i logika, 49:2 (2010), 263–290 | MR | Zbl

[7] E. I. Timoshenko, “Maltsevskaya baza chastichno kommutativnoi nilpotentnoi, metabelevoi gruppy”, Algebra i logika, 50:5 (2011), 647–658 | MR | Zbl

[8] Ch. K. Gupta, E. I. Timoshenko, “Ob universalnykh teoriyakh chastichno kommutativnykh metabelevykh grupp”, Algebra i logika, 50:1 (2011), 3–25 | MR | Zbl

[9] F. Cartier, D. Foata, Problèmes combinatoires de commutation et réarrangements, Lect. Notes Math., 85, Springer-Verlag, Berlin a. o., 1969 | DOI | MR | Zbl

[10] K. Hang Kim, L. Makar-Limanov, J. Neggers, F. W. Roush, “Graph algebras”, J. Algebra, 64 (1980), 46–51 | DOI | MR | Zbl

[11] G. Duchamp, D. Krob, “The free partially commutative Lie algebra: Bases and ranks”, Adv. Math., 92:1 (1992), 95–126 | MR | Zbl

[12] E. N. Poroshenko, “O bazisakh chastichno kommutativnykh algebrakh Li”, Algebra i logika, 50:5 (2011), 595–614 | MR | Zbl

[13] E. N. Poroshenko, “Tsentralizatory v chastichno kommutativnykh algebrakh Li”, Algebra i logika, 51:4 (2012), 524–554 | MR | Zbl

[14] E. N. Poroshenko, E. I. Timoshenko, “Universal equivalence of partially commutative metabelian Lie algebras”, J. Algebra, 384 (2013), 143–168 | DOI | MR | Zbl

[15] E. N. Poroshenko, “On universal equivalence of partially commutative metabelian Lie algebras”, Commun. Algebra, 43:2 (2015), 746–762 | DOI | MR | Zbl

[16] M. Hall, “A basis for free Lie rings and higher commutators in free groups”, Proc. Am. Math. Soc., 1 (1950), 575–581 | DOI | MR | Zbl

[17] A. I. Shirshov, “Podalgebry svobodnykh lievykh algebr”, Matem. sb., 33(75):2 (1953), 441–452 | MR | Zbl

[18] A. I. Shirshov, “O svobodnykh koltsakh Li”, Matem. sb., 45(87):2 (1958), 113–122 | MR | Zbl