nilpotent quotients in finitely presented Lie rings †
نویسندگان
چکیده
A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) 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 . LIENQ’s 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
منابع مشابه
Computing nilpotent quotients in finitely presented Lie rings
A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) 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...
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