Gröbner–Shirshov bases of the Lie algebra 𝐷⁺_{𝑛}

Koryukin, A.

doi:10.1090/S1061-0022-2011-01159-8

Gröbner–Shirshov bases of the Lie algebra $D^+_n$
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by A. N. Koryukin
Translated by: N. B. Lebedinskaya

St. Petersburg Math. J. 22 (2011), 573-614

DOI: https://doi.org/10.1090/S1061-0022-2011-01159-8

Published electronically: May 2, 2011

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Abstract:

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).

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