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Gröbner-Shirshov bases of the Lie algebra 
Author(s):
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
Posted:
November 13, 2008
MathSciNet review:
2411970
Retrieve article in:
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Abstract:
The minimal Gröbner-Shirshov bases of the positive part  of a simple finite-dimensional Lie algebra  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  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  . The minimal Gröbner-Shirshov basis of the Lie algebra  was calculated earlier by Bokut and Klein, but this was done for only one ordering of generators.
References:
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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
Email:
koryukin@ngs.ru
DOI:
10.1090/S1061-0022-08-01038-8
PII:
S 1061-0022(08)01038-8
Received by editor(s):
29/JAN/2007
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
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