Linear algebraic approach to Grobner-Shirshov basis theory

Abstract

We construct a new efficient algorithm for finding Grobner-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. Faug re. We work out some examples of universal enveloping algebras of Lie algebras and of their representations to illustrate the algorithm. (c) 2007 Elsevier Inc. All rights reserved.