Fixed-Point-Free Automorphisms of Algebraic Tori

Abstract

In the author's paper [1] there was an error in Lemma 5 which was pointed out by David J. Winter. The present paper gives a description of fixed-point-free automorphisms of algebraic tori and includes an appendix containing the necessary corrections to [1]. The reader is referred to [1] for results on Frobenius algebraic groups. We shall denote p the characteristic exponent of the ground field. A first attempt to describe the situation is in the case of a group H of fixed-point-free automorphisms of a torus T (i. e. H is an algebraic transformation group on T operating faithfully by fixed-point-free rational automorphisms).