Geodesic
Gr\"obner--Shirshov bases of the Lie algebra $B_n^+$
Algebra i analiz, Tome 20 (2008) no. 1, pp. 93-137.

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The minimal Gröbner–Shirshov bases of the positive part $B_n^+$ of the simple finite-dimensional Lie algebra $B_n$ over an arbitrary field of characteristic $0$ are calculated, for the generators associated with simple roots and for an arbitrary ordering of these generators (i.e., an arbitrary one of $n!$ Gröbner–Shirshov bases is chosen and studied). This is a completely new class of problems; till now this program was carried out only for the Lie algebra $A_n^+$. The minimal Gröbner–Shirshov basis of the Lie algebra $B_n^+$ was calculated earlier by Bokut and Klein, but this was done for only one ordering of generators. 
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A. N. Koryukin. Gr\"obner--Shirshov bases of the Lie algebra $B_n^+$. Algebra i analiz, Tome 20 (2008) no. 1, pp. 93-137. http://geodesic.mathdoc.fr/item/AA_2008_20_1_a3/

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

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

[3] Koryukin A. N., “Bazisy Grëbnera–Shirshova algebry Li $A_n$”, Algebra i logika, 44:2 (2005), 131–147 | MR | Zbl

[4] Koryukin A. N., Shum K. P., “Redutsirovannye bazisy algebry Li $D_n^+$”, Sib. zh. industr. mat., 9:4 (2006), 90–104 | MR

[5] Bokut L. A., Klein A. A., “Serre relations and Gröbner–Shirshov bases for simple Lie algebras. I”, Internat. J. Algebra Comput., 6:4 (1996), 389–400 | DOI | MR | Zbl

[6] Lalonde P., Ram A., “Standard Lyndon bases of Lie algebras and enveloping algebras”, Trans. Amer. Math. Soc., 347:5 (1995), 1821–1830 | DOI | MR | Zbl

[7] Bokut L. A., Klein A. A., “Serre relations and Gröbner–Shirshov bases for simple Lie algebras. II”, Internat. J. Algebra Comput., 6:4 (1996), 401–412 | DOI | MR | Zbl

[8] Humphreys J. E., Introduction to Lie algebras and representation theory, Grad. Texts in Math., 9, Springer-Verlag, New York–Berlin, 1972 | MR | Zbl

[9] Dzhekobson N., Algebry Li, Mir, M., 1964 | MR

[10] Burbaki N., Gruppy i algebry Li. Gruppy Kokstera i sistemy Titsa. Gruppy, porozhdennye otrazheniyami sistemy kornei, Mir, M., 1972 | MR | Zbl