Gröbner–Shirshov bases of the Lie algebra $D^+_n$

Over a field of characteristic 0, the reduced Gröbner–Shirshov bases (RGShB) are computed in the positive part $D_n^+$ of the simple finite-dimensional Lie algebra $D_n$ for the canonical generators corresponding to simple roots, under an arbitrary ordering of these generators (i.e., an aritrary basis among the $n!$ bases is fixed and analyzed). In this setting, the RGShBs were previously computed by the author for the Lie algebras $A_n^+$, $B_n^+$, and $C_n^+$. For one ordering of the generators, the RGShBs of these algebras were calculated by Bokut and Klein (1996).