On the finite generation of additive group invariants in positive characteristic
Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero, and thus, eac...
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| Format: | Journal article |
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Elsevier
2010
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| _version_ | 1797082022104006656 |
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| author | Dufresne, E Maurischat, A |
| author_facet | Dufresne, E Maurischat, A |
| author_sort | Dufresne, E |
| collection | OXFORD |
| description | Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero, and thus, each is the kernel of a locally nilpotent derivation. In positive characteristic, additive group actions correspond to locally finite iterative higher derivations. We set up characteristic-free analogs of the three examples, and show that, contrary to characteristic zero, in every positive characteristic, the invariants are finitely generated. |
| first_indexed | 2024-03-07T01:22:17Z |
| format | Journal article |
| id | oxford-uuid:90c3daf1-cbde-4b3c-87bb-ed0df8725fed |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:22:17Z |
| publishDate | 2010 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:90c3daf1-cbde-4b3c-87bb-ed0df8725fed2022-03-26T23:14:00ZOn the finite generation of additive group invariants in positive characteristicJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:90c3daf1-cbde-4b3c-87bb-ed0df8725fedSymplectic Elements at OxfordElsevier2010Dufresne, EMaurischat, ARoberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero, and thus, each is the kernel of a locally nilpotent derivation. In positive characteristic, additive group actions correspond to locally finite iterative higher derivations. We set up characteristic-free analogs of the three examples, and show that, contrary to characteristic zero, in every positive characteristic, the invariants are finitely generated. |
| spellingShingle | Dufresne, E Maurischat, A On the finite generation of additive group invariants in positive characteristic |
| title | On the finite generation of additive group invariants in positive characteristic |
| title_full | On the finite generation of additive group invariants in positive characteristic |
| title_fullStr | On the finite generation of additive group invariants in positive characteristic |
| title_full_unstemmed | On the finite generation of additive group invariants in positive characteristic |
| title_short | On the finite generation of additive group invariants in positive characteristic |
| title_sort | on the finite generation of additive group invariants in positive characteristic |
| work_keys_str_mv | AT dufresnee onthefinitegenerationofadditivegroupinvariantsinpositivecharacteristic AT maurischata onthefinitegenerationofadditivegroupinvariantsinpositivecharacteristic |