The action of an algebraic torus on the affine plane
A. Gutwirth · Transactions of the American Mathematical Society · 1962
Denote by k an algebraically closed field, by A2 the affine plane over k, by Gm the multiplicative group of the universal domain. Our purpose in this paper is to study by elementary means the regular operation of Gm on A2. We shall denote by a a regular operation of Gm on A2 which is not the identity on A2, a: Gm x A2 A2, and by Q(t) the restriction of this map given by cr(t): t x A2 -A2, where t EGm. We recall that an algebraic torus is the direct product of a finite number of multiplicative groups.