Grobner-Shirshov bases for plactic algebras

Details Grobner-Shirshov bases for plactic algebras Grobner-Shirshov bases for plactic algebras

2010-10-16

arxiv.org/abs/1010.3338v1

Mathematics

Rings and Algebras

Scientific paper

A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras, recently considered by Chen Yuqun and Qiu Jianjun.

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