Csaba Schneider - Computing nilpotent quotients in finitely presented Lie rings

dmtcs:234 - Discrete Mathematics & Theoretical Computer Science, January 1, 1997, Vol. 1 - https://doi.org/10.46298/dmtcs.234
Computing nilpotent quotients in finitely presented Lie ringsArticle

Authors: Csaba Schneider 1

  • 1 School of Mathematical Sciences [Canberra]

A nilpotent quotient algorithm for finitely presented Lie rings over \textbfZ (and \textbfQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed by generators. Using that presentation the word problem is decidable in L. Provided that the Lie ring L is graded, it is possible to determine the canonical presentation for a lower central factor of L. Complexity is studied and it is shown that optimising the presentation is NP-hard. Computational details are provided with examples, timing and some structure theorems obtained from computations. Implementation in C and GAP interface are available.


Volume: Vol. 1
Published on: January 1, 1997
Imported on: March 26, 2015
Keywords: nilpotent presentation,Lie rings,nilpotent Lie rings,finitely presented Lie rings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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