Constructing Bases of Finitely Presented Lie Algebras using Grobner Bases in Free Algebras

摘要

We derive a sufficient condition for a generating set of an ideal in the free (non-associative, non-commutative) algebra to be a Grobner basis. Using this we formulate an algorithm for computing a basis of a finitely presented Lie algebra. At the end of the paper we discuss the practical implementation of the algorithm.