A negative result of direct sum of integral symplectic matrices

作者：Yang, Qingjie^*

来源：Journal of Number Theory, 2013, 133(8): 2722-2728.

DOI：10.1016/j.jnt.2013.02.009

• Integral symplectic matrix
• Similar
• Direct sum of symplectic matrix
• Symplectic group space
• Palindromic monic polynomial

In this paper we give a result on the symplectic direct sum of symplectic matrices. For any torsion of integral symplectic matrix X with cyclotomic polynomial as its characteristic polynomial, direct sum of k copies of X is not symplectic integral similar to direct sum of k copies of X-1, the inverse of X. The tool we use is symplectic group spaces constructed by pairs of ideal and element in domain Z[zeta] with certain conditions, where Z is the ring of integers and zeta is a root of a palindromic monic irreducible polynomial.

• 出版日期2013-8
• 单位中国人民大学