A Burnside ring for monoids
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911218575343616 |
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| author | Weissmann, Jeremy |
| author_facet | Weissmann, Jeremy |
| contents | In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad class of monoids that allows us to write the Burnside ring as a direct product of Burnside rings of groups. Finally, we define a monoid correlate of the table of marks, and show that the Burnside algebra over the rationals is semisimple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15081 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Burnside ring for monoids Weissmann, Jeremy Representation Theory In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad class of monoids that allows us to write the Burnside ring as a direct product of Burnside rings of groups. Finally, we define a monoid correlate of the table of marks, and show that the Burnside algebra over the rationals is semisimple. |
| title | A Burnside ring for monoids |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2311.15081 |