The diagonal $p$-permutation functor $kR_k$
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909417516040192 |
|---|---|
| author | Bouc, Serge |
| author_facet | Bouc, Serge |
| contents | Let $k$ be an algebraically closed field of positive characteristic $p$. We describe the full lattice of subfunctors of the diagonal $p$-permutation functor $kR_k$ obtained by $k$-linear extension from the functor $R_k$ of linear representations over $k$. This leads to the description of the ``composition factors'' $S_P$ of $kR_k$, which are parametrized by finite $p$-groups (up to isomorphism), and of the evaluations of these particular simple diagonal $p$-permutation functors over $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The diagonal $p$-permutation functor $kR_k$ Bouc, Serge Group Theory Category Theory Rings and Algebras Representation Theory 16S50, 18B99, 20C20, 20J15 Let $k$ be an algebraically closed field of positive characteristic $p$. We describe the full lattice of subfunctors of the diagonal $p$-permutation functor $kR_k$ obtained by $k$-linear extension from the functor $R_k$ of linear representations over $k$. This leads to the description of the ``composition factors'' $S_P$ of $kR_k$, which are parametrized by finite $p$-groups (up to isomorphism), and of the evaluations of these particular simple diagonal $p$-permutation functors over $k$. |
| title | The diagonal $p$-permutation functor $kR_k$ |
| topic | Group Theory Category Theory Rings and Algebras Representation Theory 16S50, 18B99, 20C20, 20J15 |
| url | https://arxiv.org/abs/2412.04221 |