Hall and Grobner bases and rewriting in free Lie algebras

Abstract

Lie algebras given by generators and relations occur in my contexts. Some examples are Kao-Moody algebras, Engel and sandwich algebras and Serre’s presentation of the simple Lie algebras. In this abstract we sketch methods for rewriting elements in a Lie algebra given by generators and relations. Such an algebra is a quotient of a free algebra A by an ideal I generated by the relations. One of the main problems is computing te product of two elements in the factor A/I. This problem is solved once we have a method for rewriting elements in A modulo I.