Invariant symplectic forms on number fifields

Rafiqi A., ZEYTİN A.

Turkish Journal of Mathematics, vol.48, no.1, pp.53-61, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3491
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.53-61
  • Keywords: invariance, Number field, palindromic, symplectic form
  • Galatasaray University Affiliated: Yes

Abstract

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.).