Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures

Murray R. Bremner

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 3, page 341-379
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Bremner, Murray R.. "Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures." Commentationes Mathematicae Universitatis Carolinae 55.3 (2014): 341-379. <http://eudml.org/doc/261865>.

@article{Bremner2014,
abstract = {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.},
author = {Bremner, Murray R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
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; free associative algebras; Gröbner bases; Lie algebras; Jordan algebras; triple systems; trilinear operations; composition diamond lemma; universal associative envelopes; PBW theorem; computer algebra},
language = {eng},
number = {3},
pages = {341-379},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures},
url = {http://eudml.org/doc/261865},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Bremner, Murray R.
TI - Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 3
SP - 341
EP - 379
AB - 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.
LA - eng
KW - 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; free associative algebras; Gröbner bases; Lie algebras; Jordan algebras; triple systems; trilinear operations; composition diamond lemma; universal associative envelopes; PBW theorem; computer algebra
UR - http://eudml.org/doc/261865
ER -

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