Gröbner–Shirshov bases of the Lie algebra $B_n^+$
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A. N. Koryukin
Translated by: A. V. Yakovlev - St. Petersburg Math. J. 20 (2009), 65-94
- DOI: https://doi.org/10.1090/S1061-0022-08-01038-8
- Published electronically: November 13, 2008
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Abstract:
The minimal Gröbner–Shirshov bases of the positive part $B_n^+$ of a simple finite-dimensional Lie algebra $B_n$ over an arbitrary field of characteristic $0$ are calculated, for the generators associated with simple roots and for an arbitrary ordering of these generators (i.e., an arbitrary basis of the $n!$ Gröbner–Shirshov bases is chosen and studied). This is a completely new class of problems; until now, this program was carried out only for the Lie algebra $A_n^+$. The minimal Gröbner–Shirshov basis of the Lie algebra $B_n^+$ was calculated earlier by Bokut and Klein, but this was done for only one ordering of generators.References
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Bibliographic Information
- A. N. Koryukin
- Affiliation: Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 4 Academician Koptyug Avenue, 630090, Novosibirsk, Russia
- Email: koryukin@ngs.ru
- Received by editor(s): January 29, 2007
- Published electronically: November 13, 2008
- Additional Notes: The work was partially supported by RFBR (grant no. 05-01-00230), by the Leading Scientific Schools Foundation (grant no. 2069.20031), and by the Complex Integration Projects Foundation of the Siberian Branch of RAS
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 20 (2009), 65-94
- MSC (2000): Primary 17Bxx
- DOI: https://doi.org/10.1090/S1061-0022-08-01038-8
- MathSciNet review: 2411970