Hopf Algebra Structure of mod 2 Cohomology of Simple Lie Groups

The purpose of the present paper is to determine the Hopf algebra structure of the mod 2 cohomology JJ*(G; Z2) of each compact connected simple Lie group G. For classical type G, the Hopf algebra H* (G; Z2) is determined by Borel [6] and Baum-Browder [3], except the spinor groups Spin(n) and the semi-spinor groups ,5s (4m). For exceptional type G, it is determined by several authors [6], [8], [9], [15], except the case G = AdE7 = E7/Zz. In order to describe our results, we shall use the submodule TG* of /J*(G;Zp) which consists of the transgressive elements with respect to the fibering