में बचाया:
| मुख्य लेखकों: | , |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2026
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2604.04337 |
| टैग: |
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| _version_ | 1866918429877862400 |
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| author | Cid, Luis Veloso, Marcelo |
| author_facet | Cid, Luis Veloso, Marcelo |
| contents | Let K be an algebraically closed field of characteristic zero. We study the tame isotropy group Tame_D(K[X,Y]) of locally finite derivations of the polynomial ring K[X,Y], using Van den Essen's classification up to conjugation. For each normal form, we explicitly determine the corresponding tame isotropy group. We then compare Tame_D(K[X,Y]) with the tame isotropy group of the associated exponential automorphism exp(D), and prove that these groups always coincide. This stands in contrast to the behaviour of the full automorphism group, where such an equality may fail for derivations with a nontrivial semisimple part. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04337 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Tame Isotropy Group of Locally Finite Derivations of K[X,Y] Cid, Luis Veloso, Marcelo Algebraic Geometry Commutative Algebra 13N15, 14R10, 13B10 Let K be an algebraically closed field of characteristic zero. We study the tame isotropy group Tame_D(K[X,Y]) of locally finite derivations of the polynomial ring K[X,Y], using Van den Essen's classification up to conjugation. For each normal form, we explicitly determine the corresponding tame isotropy group. We then compare Tame_D(K[X,Y]) with the tame isotropy group of the associated exponential automorphism exp(D), and prove that these groups always coincide. This stands in contrast to the behaviour of the full automorphism group, where such an equality may fail for derivations with a nontrivial semisimple part. |
| title | On the Tame Isotropy Group of Locally Finite Derivations of K[X,Y] |
| topic | Algebraic Geometry Commutative Algebra 13N15, 14R10, 13B10 |
| url | https://arxiv.org/abs/2604.04337 |