Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids

Cain, Alan J., Gray, Robert and Malheiro, António (2015) Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids. Journal of Algebra, 423. 37–53. ISSN 0021-8693

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Abstract

This paper shows that every Plactic algebra of finite rank admits a finite Gröbner–Shirshov basis. The result is proved by using the combinatorial properties of Young tableaux to construct a finite complete rewriting system for the corresponding Plactic monoid, which also yields the corollaries that Plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right FP∞FP∞. Also, answering a question of Zelmanov, we apply this rewriting system and other techniques to show that Plactic monoids of finite rank are biautomatic.

Item Type: Article
Uncontrolled Keywords: plactic algebra,plactic monoid,gröbner–shirshov basis,complete rewriting system,young tableau,automatic monoids
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 10 Nov 2014 16:06
Last Modified: 22 Jul 2020 00:03
URI: https://ueaeprints.uea.ac.uk/id/eprint/50727
DOI: 10.1016/j.jalgebra.2014.09.037

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