Ideals of some Green biset functors
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909121058439168 |
|---|---|
| author | Calderón, J. Miguel |
| author_facet | Calderón, J. Miguel |
| contents | In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of M C-group, this definition generalizes that of a B-group, given for the Burnside functor. Given a Green biset functor A, with the above hypotheses, the set of all M C-groups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the M C-groups of A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ideals of some Green biset functors Calderón, J. Miguel Group Theory 16Y99, 18D99, 20J15 In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of M C-group, this definition generalizes that of a B-group, given for the Burnside functor. Given a Green biset functor A, with the above hypotheses, the set of all M C-groups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the M C-groups of A. |
| title | Ideals of some Green biset functors |
| topic | Group Theory 16Y99, 18D99, 20J15 |
| url | https://arxiv.org/abs/2402.17053 |