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Article

Bremner, Murray R.
Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 55 (2014), issue 3, pp. 341-379
MSC: 16S10, 16S30, 16W10, 16Z05, 17A30, 17A40, 17A42, 17B35, 17B60, 17C05, 17C50, 68W30 | MR 3225614 | Zbl 06391547
Keywords:
free associative algebras; Gröbner bases; composition (diamond) lemma; universal associative envelopes; Lie algebras and triple systems; PBW theorem; Jordan algebras and triple systems; trilinear operations; computer algebra
Summary:
First, we provide an introduction to the theory and algorithms for noncommutative Gröbner bases for ideals in free associative algebras. Second, we explain how to construct universal associative envelopes for nonassociative structures defined by multilinear operations. Third, we extend the work of Elgendy (2012) for nonassociative structures on the 2-dimensional simple associative triple system to the 4- and 6-dimensional systems.
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