| Title: | A new approach to universal $F$-inverse monoids in enriched signature |
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| Authors: | ID Kudryavtseva, Ganna (Author)
ID Lemut Furlani, Ajda (Author) |
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| Files: |  PDF - Presentation file, download (347,64 KB)
MD5: 8BC86DECDD2A8C17712D8BE633DC1036
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00025-024-02291-4
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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 ${\rm Cay}(G, X\cup {\overline{G}})$ and leads to a new and simpler proof of the universal property of $F(G)$. |
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| Keywords: | inverse monoid, F-inverse monoid, Margolis-Meakin expansion, group presentation, Cayley graph of a group, closure operator, dual-closure operator, partial action, partial action product |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.11.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 13 str. |
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| Numbering: | Vol. 79, iss. 7, [article no.] 260 |
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| PID: | 20.500.12556/DiRROS-20546  |
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| UDC: | 512 |
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| ISSN on article: | 1422-6383 |
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| DOI: | 10.1007/s00025-024-02291-4 |
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| COBISS.SI-ID: | 211681795 |
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| Note: |
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| Publication date in DiRROS: | 21.10.2024 |
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| Views: | 137 |
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| Downloads: | 58 |
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