On the bilinear structure associated to Bezoutians

JOURNAL OF ALGEBRA

卷:400

Article

Jouve, F.¹  Villegas, F. Rodriguez^2,3 

[1] Univ Paris 11, Fac Sci Orsay, Dept Math, F-91405 Orsay, France

[2] Abdus Salam Int Ctr Theoret Phys, I-34151 Trieste, Italy

[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

关键词: Bilinear forms;    Bezoutian of polynomials;    Characteristic polynomials;    Jordan form of isometries;   

DOI  :  10.1016/j.jalgebra.2013.10.030

来源: Elsevier

【 摘 要 】

This paper is partly a survey of known results on quadratic forms that are hard to find in the literature. Our main focus is a twisted form of a construction due to Bezout. This skew Bezoutian is a symplectic (resp. quadratic) space associated to a pair of reciprocal (or skew reciprocal) coprime polynomials of same degree. The isometry group of this space turns out to contain a certain associated hypergeometric group. Using the skew Bezoutian we construct explicit isometries of bilinear spaces with given invariants (such as the characteristic polynomial or Jordan form and, in the quadratic case, the spinor norm). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free