Representations and identities of plactic-like monoids

Cain, Alan J.; Johnson, Marianne; Kambites, Mark; Malheiro, António

doi:https://doi.org/10.1016/j.jalgebra.2022.04.033

Utilize este identificador para referenciar este registo: http://hdl.handle.net/10362/145310

Título:	Representations and identities of plactic-like monoids
Autor:	Cain, Alan J. Johnson, Marianne Kambites, Mark Malheiro, António
Palavras-chave:	Baxter monoid Hypoplactic monoid Plactic monoid Representation Semigroup identity Stalactic monoid Sylvester monoid Taiga monoid Tropical semiring Upper triangular matrix semigroup Varieties Algebra and Number Theory
Data:	15-Set-2022
Citação:	Cain, A. J., Johnson, M., Kambites, M., & Malheiro, A. (2022). Representations and identities of plactic-like monoids. Journal of Algebra, 606, 819-850. https://doi.org/10.1016/j.jalgebra.2022.04.033
Resumo:	We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of characteristic 0. By analysing the image of these representations, we show that the variety generated by a single hypoplactic (respectively, stalactic or taiga) monoid of rank at least 2 coincides with the variety generated by the natural numbers together with a fixed finite monoid H (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2.
Descrição:	Publisher Copyright: © 2022
Peer review:	yes
URI:	http://hdl.handle.net/10362/145310
DOI:	https://doi.org/10.1016/j.jalgebra.2022.04.033
ISSN:	0021-8693
Aparece nas colecções:	FCT: CMA - Artigos em revista internacional com arbitragem científica

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