Tensor Product and the Stable Green Ring of the Symmetric Group Algebra $F\mathfrak{S}_p$
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908969334734848 |
|---|---|
| author | Kua, Manzu Lim, Kay Jin |
| author_facet | Kua, Manzu Lim, Kay Jin |
| contents | We give an explicit formula for the decomposition of the tensor product of any two indecomposable non-projective modules for the symmetric group algebra $F \mathfrak{S}_p$ modulo projective modules. In particular, we show that the tensor product of two simple modules is semisimple modulo projectives. We also compute the Benson--Symonds invariants for all such indecomposable non-projective modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11533 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor Product and the Stable Green Ring of the Symmetric Group Algebra $F\mathfrak{S}_p$ Kua, Manzu Lim, Kay Jin Representation Theory Rings and Algebras 20C30, 20C05, 18G65 We give an explicit formula for the decomposition of the tensor product of any two indecomposable non-projective modules for the symmetric group algebra $F \mathfrak{S}_p$ modulo projective modules. In particular, we show that the tensor product of two simple modules is semisimple modulo projectives. We also compute the Benson--Symonds invariants for all such indecomposable non-projective modules. |
| title | Tensor Product and the Stable Green Ring of the Symmetric Group Algebra $F\mathfrak{S}_p$ |
| topic | Representation Theory Rings and Algebras 20C30, 20C05, 18G65 |
| url | https://arxiv.org/abs/2603.11533 |