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


Author: A. N. Koryukin
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 22 (2010), nomer 4.
Journal: St. Petersburg Math. J. 22 (2011), 573-614
MSC (2010): Primary 17B22
DOI: https://doi.org/10.1090/S1061-0022-2011-01159-8
Published electronically: May 2, 2011
MathSciNet review: 2768962
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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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Additional Information

A. N. Koryukin
Affiliation: Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Academician Koptyug Avenue 4, Novosibirsk 630090, Russia
Email: koryukin@ngs.ru

DOI: https://doi.org/10.1090/S1061-0022-2011-01159-8
Keywords: Gröbner–Shirshov, bases Lie algebras
Received by editor(s): March 18, 2009
Published electronically: May 2, 2011
Article copyright: © Copyright 2011 American Mathematical Society

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