Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition, II

Authors:
Serena Cicalò;Willem A. de Graaf
Affiliations:
Dipartimento di Matematica, Università di Trento, Italy;Dipartimento di Matematica, Università di Trento, Italy
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

We give an algorithm for constructing a basis and a multiplication table of a finite-dimensional finitely-presented Lie ring. Secondly, we give relations that are equivalent to the n-Engel condition, and only have to be checked for the elements of a basis of a Lie ring. We apply this to construct the freest t-generator Lie rings that satisfy the n-Engel condition, for (t,n)=(2,3),(3,3),(4,3),(2,4).