The separating variety for the basic representations of the additive group
For a group G acting on an affine variety X, the separating variety is the closed subvariety of X×X encoding which points of X are separated by invariants. We concentrate on the indecomposable rational linear representations Vn of dimension n+1 of the additive group of a field of characteristic zero...
| Main Authors: | , |
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| Format: | Journal article |
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Elsevier
2013
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| _version_ | 1797058012867723264 |
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| author | Dufresne, E Kohls, M |
| author_facet | Dufresne, E Kohls, M |
| author_sort | Dufresne, E |
| collection | OXFORD |
| description | For a group G acting on an affine variety X, the separating variety is the closed subvariety of X×X encoding which points of X are separated by invariants. We concentrate on the indecomposable rational linear representations Vn of dimension n+1 of the additive group of a field of characteristic zero, and decompose the separating variety into the union of irreducible components. We show that if n is odd, divisible by four, or equal to two, the closure of the graph of the action, which has dimension n+2, is the only component of the separating variety. In the remaining cases, there is a second irreducible component of dimension n+1. We conclude that in these cases, there are no polynomial separating algebras. |
| first_indexed | 2024-03-06T19:44:35Z |
| format | Journal article |
| id | oxford-uuid:21d573c8-d352-496e-b742-816afefb4712 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:44:35Z |
| publishDate | 2013 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:21d573c8-d352-496e-b742-816afefb47122022-03-26T11:35:35ZThe separating variety for the basic representations of the additive groupJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:21d573c8-d352-496e-b742-816afefb4712Symplectic Elements at OxfordElsevier2013Dufresne, EKohls, MFor a group G acting on an affine variety X, the separating variety is the closed subvariety of X×X encoding which points of X are separated by invariants. We concentrate on the indecomposable rational linear representations Vn of dimension n+1 of the additive group of a field of characteristic zero, and decompose the separating variety into the union of irreducible components. We show that if n is odd, divisible by four, or equal to two, the closure of the graph of the action, which has dimension n+2, is the only component of the separating variety. In the remaining cases, there is a second irreducible component of dimension n+1. We conclude that in these cases, there are no polynomial separating algebras. |
| spellingShingle | Dufresne, E Kohls, M The separating variety for the basic representations of the additive group |
| title | The separating variety for the basic representations of the additive group |
| title_full | The separating variety for the basic representations of the additive group |
| title_fullStr | The separating variety for the basic representations of the additive group |
| title_full_unstemmed | The separating variety for the basic representations of the additive group |
| title_short | The separating variety for the basic representations of the additive group |
| title_sort | separating variety for the basic representations of the additive group |
| work_keys_str_mv | AT dufresnee theseparatingvarietyforthebasicrepresentationsoftheadditivegroup AT kohlsm theseparatingvarietyforthebasicrepresentationsoftheadditivegroup AT dufresnee separatingvarietyforthebasicrepresentationsoftheadditivegroup AT kohlsm separatingvarietyforthebasicrepresentationsoftheadditivegroup |