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arXiv · 1808.01579

Products of involutions in the stable general linear group

Clément de Seguins Pazzis
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Abstract

In the stable general linear group over an arbitrary field, we prove that every element with determinant $\pm 1$ is the product of three involutions, and of no less in general. We also obtain several results of the same flavor, with applications to decompositions of automorphisms of an infinite-dimensional vector space that are scalar multiples of finite-rank perturbations of the identity.

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Clément de Seguins Pazzis. 2018-08-05. Products of involutions in the stable general linear group. https://arxiv.org/abs/1808.01579

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