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Algebra i Analiz, 2010, Volume 22, Issue 4, Pages 76–136 (Mi aa1198)  

This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

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

A. N. Koryukin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

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).

Keywords: Gröbner–Shirshov, bases Lie algebras.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:4, 573–614

Bibliographic databases:

Received: 18.03.2009

Citation: A. N. Koryukin, “Gröbner–Shirshov bases of the Lie algebra $D^+_n$”, Algebra i Analiz, 22:4 (2010), 76–136; St. Petersburg Math. J., 22:4 (2011), 573–614

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Koryukin A.N., “Sistemy kornei, redutsirovannye slova i polnye redutsirovannye sistemy sootnoshenii algebr Li”, Dokl. Akademii nauk vysshei shkoly RF, 2011, no. 2, 15–24  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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