A new approach to universal $F$-inverse monoids in enriched signature
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916455584366592 |
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| author | Kudryavtseva, Ganna Furlani, Ajda Lemut |
| author_facet | Kudryavtseva, Ganna Furlani, Ajda Lemut |
| contents | We show that the universal $X$-generated $F$-inverse monoid $F(G)$, where $G$ is an $X$-generated group, introduced by Auinger, Szendrei and the first-named author, arises as a quotient inverse monoid of the Margolis-Meakin expansion $M(G, X\cup \overline{G})$ of $G$, with respect to the extended generating set $X\cup \overline{G}$, where $\overline{G}$ is a bijective copy of $G$ which encodes the $m$-operation in $F(G)$. The construction relies on a certain dual-closure operator on the semilattice of all finite and connected subgraphs containing the origin of the Cayley graph $Cay(G, X\cup {\overline{G}})$ and leads to a new and simpler proof of the universal property of $F(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new approach to universal $F$-inverse monoids in enriched signature Kudryavtseva, Ganna Furlani, Ajda Lemut Group Theory Rings and Algebras 20M18, 20M10, 20F05, 05E18 We show that the universal $X$-generated $F$-inverse monoid $F(G)$, where $G$ is an $X$-generated group, introduced by Auinger, Szendrei and the first-named author, arises as a quotient inverse monoid of the Margolis-Meakin expansion $M(G, X\cup \overline{G})$ of $G$, with respect to the extended generating set $X\cup \overline{G}$, where $\overline{G}$ is a bijective copy of $G$ which encodes the $m$-operation in $F(G)$. The construction relies on a certain dual-closure operator on the semilattice of all finite and connected subgraphs containing the origin of the Cayley graph $Cay(G, X\cup {\overline{G}})$ and leads to a new and simpler proof of the universal property of $F(G)$. |
| title | A new approach to universal $F$-inverse monoids in enriched signature |
| topic | Group Theory Rings and Algebras 20M18, 20M10, 20F05, 05E18 |
| url | https://arxiv.org/abs/2402.12313 |