A new approach to universal $F$-inverse monoids in enriched signature

Kudryavtseva, Ganna (author), Lemut Furlani, Ajda (author)

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 $F(G)$.

• Language: English
• 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
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 13 str.
• Numbering: Vol. 79, iss. 7, art. 260
• PID: 20.500.12556/RUL-164079
• UDC: 512
• ISSN on article: 1422-6383
• DOI: 10.1007/s00025-024-02291-4
• COBISS.SI-ID: 211681795
• Publication date in RUL: 16.10.2024

Record is a part of a journal

• Title: Results in mathematics
• Shortened title: Results math.
• Publisher: Springer Nature
• ISSN: 1422-6383
• COBISS.SI-ID: 514963225

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: inverzni monoid, F-invezni monoid, Margolis-Meakin razširjanje, grupna prezentacija, Cayleyjev graf grupe, operator zaprtja, dualni operator zaprtja, parcialno delovanje, produkt glede na parcialno delovanje

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0288
• Name: Algebra in njena uporaba