On the homology of the Kac-Moody groups and the cohomology of the 3-connective covers of Lie groups (Q1872577)

Let \(G= F_4\), \(E_6\), \(E_7\) or \(E_8\) and denote by \(\widetilde G\) the 3-connective cover over \(G\). Recall that the Kac-Moody group \(K(g^{(1)})\) is the central extension by \(S^1\) of the space of free loops in \(G\). In this paper, the author determines \(H_*(K(g^{(1)}; \mathbb{F}_3)\) and \(H^*(\widetilde G;\mathbb{F}_3)\) as Hopf algebras over the Steenrod algebra \({\mathcal A}_3\). A similar result is given for \(E_8\) at prime \(5\).