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TitleLinear algebraic approach to Gröbner–Shirshov basis theory
Author(s) Seok-Jin Kang, Dong-il Lee, Kyu-Hwan Lee, Hyungju Park
TypeArticle in Journal
AbstractWe construct a new efficient algorithm for finding Gröbner–Shirshov bases for noncommutative algebras and their representations. This algorithm uses the Macaulay matrix [F.S. Macaulay, On some formula in elimination, Proc. London Math. Soc. 33 (1) (1902) 3–27], and can be viewed as a representation theoretic analogue of the F 4 algorithm developed by J.C. Faugère. We work out some examples of universal enveloping algebras of Lie algebras and of their representations to illustrate the algorithm.
KeywordsGröbner–Shirshov basis, Gröbner–Shirshov pair, Monomial basis
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869307000798
LanguageEnglish
JournalJournal of Algebra
Volume313
Number2
Pages988 - 1004
Year2007
Edition0
Translation No
Refereed No
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