Details:
Title  Linear algebraic approach to Gröbner–Shirshov basis theory  Author(s)  SeokJin Kang, Dongil Lee, KyuHwan Lee, Hyungju Park  Type  Article in Journal  Abstract  We 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.  Keywords  Gröbner–Shirshov basis, Gröbner–Shirshov pair, Monomial basis  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869307000798 
Language  English  Journal  Journal of Algebra  Volume  313  Number  2  Pages  988  1004  Year  2007  Edition  0  Translation 
No  Refereed 
No 
