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Varieties Generated by Plactic-like Monoids: Identities and Representations
- Speaker(s)
- António Malheiro
- Affiliation
- NOVA School of Science and Technology, Lisbon
- Language of the talk
- English
- Date
- June 5, 2025, 1:30 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1
- Information about the event
- referat online
- Seminar
- Seminar Algebra
Plactic-like monoids — such as the hypoplactic, stalactic, taiga, sylvester, and Baxter monoids — arise naturally in algebraic combinatorics and exhibit rich algebraic behavior in terms of the identities they satisfy and the varieties they generate. This talk presents a unified approach to understanding the equational theories of these monoids, including complete characterizations of their identities and the construction of finite bases for the corresponding varieties.
A central aspect of this work is the use of embeddings into direct products of lower-rank monoids, which allows the reduction of identity questions to the rank-two case. These structural results are complemented by faithful representations over tropical and other semirings, which shed light on the algebraic properties of these monoids and clarify their place within the lattice of semigroup varieties.
Recent developments also include the study of new plactic-like structures arising from natural congruence operations, as well as further analysis of the varieties they generate. Together, these results contribute to a broader understanding of the interplay between combinatorial constructions and semigroup identities.
These results are part of joint work with Alan Cain, Marianne Johnson, Mark Kambites, and Duarte Ribeiro.
