Turkish Journal of Mathematics
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) .
DOI
10.55730/1300-0098.3491
Keywords
Number field, symplectic form, invariance, palindromic
First Page
53
Last Page
61
Recommended Citation
RAFIQI, A, & ZEYTİN, A (2024). Invariant symplectic forms on number fields. Turkish Journal of Mathematics 48 (1): 53-61. https://doi.org/10.55730/1300-0098.3491
