Polynomial maps with constants on split octonion algebras

Abstract

Let O(F) be the split octonion algebra over an algebraically closed field F. For positive integers k(1), k(2) >= 2, we study surjectivity of the map A(1)(x(1)(k)) + A(2)(y(2)(k)) is an element of O(F)< x, y > on O(F). For this, we use the orbit representatives of the G2(F)-action on O(F) x O(F) for the tuple (A(1), A(2)), and characterize the ones which give a surjective map.