Characteristic Polynomials in Clifford Algebras and in More General Algebras

Jacques Helmstetter (1)

1 IF - Institut Fourier

This article combines two independent theories: firstly, the algorithm of Faddeev–Leverrier which calculates characteristic polynomials of matrices, secondly, the Descent Theory which, in particular, lets many properties of matrix algebras descend down to Azumaya algebras, especially the characteristic polynomials. The algorithm of Faddeev–Leverrier is completely revisited. The details of the descent are explained as far as they are needed for Clifford algebras over fields.

Mots clés: Matrices; Algorithm of Faddeev–Leverrier; Central simple algebras; Azumaya algebras

Domaines: Physique mathématique [math-ph]

Jacques Helmstetter. Characteristic Polynomials in Clifford Algebras and in More General Algebras. 11th International Conference on Clifford Algebras and Their Applications in Mathematical Physics, Aug 2017, Ghent, Belgium. pp.30, ⟨10.1007/s00006-019-0944-5⟩. ⟨hal-02058574⟩