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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Gröbner-Shirshov bases of the Lie algebra $ B_n^+$

Author: A. N. Koryukin
Translated by: A. V. Yakovlev
Original publication: Algebra i Analiz, tom 20 (2008), nomer 1.
Journal: St. Petersburg Math. J. 20 (2009), 65-94
MSC (2000): Primary 17Bxx
Published electronically: November 13, 2008
MathSciNet review: 2411970
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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.

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Additional Information

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

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
Article copyright: © Copyright 2008 American Mathematical Society