Free associative algebras, noncommutative Gr\"obner bases, and universal associative envelopes for nonassociative structures

Commentationes mathematicae Universitatis Carolinae

Murray R. Bremner¹ 

关键词: free associative algebras;    Gr\"obner bases;    composition (diamond) lemma;    universal associative envelopes;    Lie algebras and triple systems;    PBW theorem;    Jordan algebras and triple systems;    trilinear operations;    computer algebra;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

First, we provide an introduction to the theory and algorithms for noncommutative Gr\"obner 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.

【 授权许可】

CC BY