Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3491
Abstract
We show that a number field of the form Q(λ) 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 Q(λ) .
Keywords
Number field, symplectic form, invariance, palindromic
First Page
53
Last Page
61
Recommended Citation
RAFIQI, AHMAD and ZEYTİN, AYBERK
(2024)
"Invariant symplectic forms on number fields,"
Turkish Journal of Mathematics: Vol. 48:
No.
1, Article 6.
https://doi.org/10.55730/1300-0098.3491
Available at:
https://journals.tubitak.gov.tr/math/vol48/iss1/6
