1. Representations and identities of Baxter monoids with involution
- Author
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Han, Bin Bin, Zhang, Wen Ting, Luo, Yan Feng, and Zhao, Jin Xing
- Subjects
FOS: Mathematics ,Group Theory (math.GR) ,Representation Theory (math.RT) ,Mathematics - Group Theory ,Mathematics - Representation Theory ,20M07, 20M30, 05E99, 12K10, 16Y60 - Abstract
Let $(\mathsf{baxt}_n,~^\sharp)$ be the Baxter monoid of finite rank $n$ with Sch\"{u}tzenberger's involution $^{\sharp}$. In this paper, it is shown that $(\mathsf{baxt}_n,~^\sharp)$ admits a faithful representation by an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. Then a transparent combinatorial characterization of the word identities satisfied by $(\mathsf{baxt}_n,~^\sharp)$ is given. Further, it is proved that $(\mathsf{baxt}_n,~^\sharp)$ is finitely based if and only if $n\neq 3$, and shown that the identity checking problem for $(\mathsf{baxt}_n,~^\sharp)$ can be done in polynomial time., Comment: arXiv admin note: substantial text overlap with arXiv:2301.12449
- Published
- 2023
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