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Products of Involutions of an Infinite-dimensional Vector Space

Published online by Cambridge University Press:  15 November 2019

Clément de Seguins Pazzis*
Affiliation:
Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques de Versailles, 45 avenue des Etats-Unis, 78035Versailles cedex, France Email: dsp.prof@gmail.com

Abstract

We prove that every automorphism of an infinite-dimensional vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are the product of three involutions. More generally, we study decompositions of automorphisms into three or four factors with prescribed split annihilating polynomials of degree $2$.

MSC classification

Type
Article
Copyright
© Canadian Mathematical Society 2019

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