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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.14511 |
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| _version_ | 1866916658739675136 |
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| author | Ruiz-Medina, Ramon H- Lara-Gómez, Victor M. |
| author_facet | Ruiz-Medina, Ramon H- Lara-Gómez, Victor M. |
| contents | For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition. The Green Relations are powerful tools to comprehend the structure of a semigroup. We study the case where $X$ is a finite set and compute the green relations for its monoid of $G$-equivariant functions, attempting to describe them based on some particular elements in the monoid called elementary collapsings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Green relations over finite monoids of $G$-equivariant functions Ruiz-Medina, Ramon H- Lara-Gómez, Victor M. Group Theory For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition. The Green Relations are powerful tools to comprehend the structure of a semigroup. We study the case where $X$ is a finite set and compute the green relations for its monoid of $G$-equivariant functions, attempting to describe them based on some particular elements in the monoid called elementary collapsings. |
| title | Green relations over finite monoids of $G$-equivariant functions |
| topic | Group Theory |
| url | https://arxiv.org/abs/2503.14511 |