Geodesic
The Right-Normed Basis for a Free Lie Superalgebra and Lyndon--Shirshov Words
Algebra i logika, Tome 45 (2006) no. 4, pp. 458-483.

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

We construct a basis for a free Lie superalgebra consisting of right-normed words $[a_{i_{1}}[a_{i_{2}}[\dots[a_{i_{t-1}}a_{i_{t}}]\dots]]]$, where $a_{i_{j}}$ are free generators.
Keywords: Lie algebra, Lyndon–Shirshov words, Lie superalgebra, basis. 
@article{AL_2006_45_4_a5,
     author = {E. S. Chibrikov},
     title = {The {Right-Normed} {Basis} for a {Free} {Lie} {Superalgebra} and {Lyndon--Shirshov} {Words}},
     journal = {Algebra i logika},
     pages = {458--483},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_4_a5/}
}
TY  - JOUR
AU  - E. S. Chibrikov
TI  - The Right-Normed Basis for a Free Lie Superalgebra and Lyndon--Shirshov Words
JO  - Algebra i logika
PY  - 2006
SP  - 458
EP  - 483
VL  - 45
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2006_45_4_a5/
LA  - ru
ID  - AL_2006_45_4_a5
ER  - 
%0 Journal Article
%A E. S. Chibrikov
%T The Right-Normed Basis for a Free Lie Superalgebra and Lyndon--Shirshov Words
%J Algebra i logika
%D 2006
%P 458-483
%V 45
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2006_45_4_a5/
%G ru
%F AL_2006_45_4_a5
E. S. Chibrikov. The Right-Normed Basis for a Free Lie Superalgebra and Lyndon--Shirshov Words. Algebra i logika, Tome 45 (2006) no. 4, pp. 458-483. http://geodesic.mathdoc.fr/item/AL_2006_45_4_a5/

[1] 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

[2] A. I. Shirshov, Nekotorye voprosy teorii neassotsiativnykh kolets i al- gebr. Avtoreferat diss. k.f.-m. n., MGU, Moskva, 1953

[3] A. I. Shirshov, “O bazakh svobodnoi algebry Li”, Algebra i logika, 1:1 (1962), 14–19 | MR | Zbl

[4] A. I. Shirshov, “O svobodnykh koltsakh Li”, Mat. cb., 45(87):2 (1958), 113–122 | Zbl

[5] K. T. Chen, R. H. Fox, R. C. Lyndon, “Free differential calculus. IV: The quotient groups of the lower central series”, Ann. Math., 68:2 (1958), 81–95 | DOI | MR

[6] L. A. Bokut, G. P. Kukin, Algorithmic and combinatorial algebra, Math. Appl. (Dordrecht), 255, Kluwer Acad. Publ., Dordrecht, 1994 | MR | Zbl

[7] A. A. Mikhalev, “Bazisy svobodnykh tsvetnykh algebr”, Vestn. MGU, 94:5 (1984)

[8] A. S. Shtern, “Svobodnye superalgebry Li”, Sib. matem. zh., 27:1 (1986), 170–174 | MR | Zbl

[9] Yu. A. Bahturin, A. A. Mikhalev, V. M. Petrogradsky, M. V. Zaicev, Infinite dimensional Lie superalgebras, De Gruyter Expo. Math., 7, Walter de Gruyter Co., Berlin, 1992 | MR

[10] G. P. Kukin, “Bazy svobodnoi algebry Li”, Matem. zametki, 24:3 (1978), 375–382 | MR | Zbl

[11] E. S. Chibrikov, “Pravonormirovannyi bazis svobodnoi algebry Li”, Dokl. RAN, 400:1 (2005), 32–34 | MR

[12] R. C. Lyndon, “On Burnside's problem I”, Trans. Am. Math. Soc., 77 (1954), 202–215 | DOI | MR | Zbl