Non-associative gröbner bases, finitely-presented lie rings and the engel condition

Abstract

We give an algorithm for constructing a basis and a multiplication table of a finite-dimensional finitely-presented Lie ring. We apply this to construct the biggest t generator Lie rings that satisfy the n-Engel condition, for (t, n) = (t, 2), (2, 3), (3, 3), (2, 4).

Engel conditions and symmetric tensors

“…Before giving our proof of Theorem 1 we briefly digress on its original proof in [CdG07,CdG09]. The longest part of the proof, given in [CdG09], consists in showing that all the conditions in (1.3) are consequences of their small subset in (1.2).…”

“…Serena Cicalò and Willem de Graaf [CdG07,CdG09] have recently developed algorithmic tools to investigate finitely presented Lie rings. They also have shown their effectiveness by applying them to a computational study of some finitely generated Lie rings satisfying an Engel condition.…”