Geodesic
Gr\"obner--Shirshov Bases for the Lie Algebra
Algebra i logika, Tome 44 (2005) no. 2, pp. 131-147.

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We estimate Gröbner–Shirshov bases for the Lie algebra $A_n$ given arbitrary orders of generators (nodes of a Dynkin graph). Previously, the Gröbner–Shirshov basis was computed in [1] for the particular case where nodes of the Dynkin graph are ordered successively.
Keywords: Lie algebra, Gröbner–Shirshov basis. 
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A. N. Koryukin. Gr\"obner--Shirshov Bases for the Lie Algebra. Algebra i logika, Tome 44 (2005) no. 2, pp. 131-147. http://geodesic.mathdoc.fr/item/AL_2005_44_2_a0/

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