Invariant symplectic forms on number fields

被引：0

作者：

Rafiqi, Ahmad ^{[1
]}

Zeytin, Ayberk ^{[2
]}

机构：

[1] Amer Univ Sharjah, Coll Arts & Sci, Dept Math & Stat, Sharjah, U Arab Emirates

[2] Galatasaray Univ, Fac Sci, Dept Math, Istanbul, Turkiye

来源：

TURKISH JOURNAL OF MATHEMATICS | 2024年 / 48卷 / 01期

关键词：

Number field; symplectic form; invariance; palindromic;

D O I：

10.55730/1300-0098.3491

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a number field of the form Q(lambda) admits a symplectic form which is invariant under multiplication by lambda if and only if the minimal polynomial of lambda is palindromic of even degree. In particular, if lambda is an algebraic integer, it is forced to be a unit. In the case when the minimal polynomial of lambda is palindromic of degree 2d, we show that there is a d -dimensional space of invariant symplectic forms on Q(lambda).

引用

页码：53 / 61

页数：10

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