Separating polynomial invariants over non-closed fields of finite abelian groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908427410735104 |
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| author | Domokos, Mátyás |
| author_facet | Domokos, Mátyás |
| contents | It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating invariants for representations of finite abelian groups over algebraically closed base fields of non-modular characteristic is generalized for the case of base fields that are not algebraically closed (like the fields of real or rational numbers). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separating polynomial invariants over non-closed fields of finite abelian groups Domokos, Mátyás Commutative Algebra Representation Theory Primary 13A50, Secondary 13P15, 20C15, 94A12 It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating invariants for representations of finite abelian groups over algebraically closed base fields of non-modular characteristic is generalized for the case of base fields that are not algebraically closed (like the fields of real or rational numbers). |
| title | Separating polynomial invariants over non-closed fields of finite abelian groups |
| topic | Commutative Algebra Representation Theory Primary 13A50, Secondary 13P15, 20C15, 94A12 |
| url | https://arxiv.org/abs/2506.22889 |