Invariant symplectic forms on number fifields
Turkish Journal of Mathematics, cilt.48, sa.1, ss.53-61, 2024 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 48 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.55730/1300-0098.3491
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.53-61
- Anahtar Kelimeler: invariance, Number field, palindromic, symplectic form
- Galatasaray Üniversitesi Adresli: Evet
Özet
We show that a number field of the form (Formula presented.)admits a symplectic form which is invariant under multiplication by λ if and only if the minimal polynomial of λ is palindromic of even degree. In particular, if λ is an algebraic integer, it is forced to be a unit. In the case when the minimal polynomial of λ is palindromic of degree 2d, we show that there is a d-dimensional space of invariant symplectic forms on (Formula presented.).