## Lab Notes on the exceptional Lie group E8 at the prime 2

Citations: | 1 - 0 self |

### BibTeX

@MISC{Wilkerson_labnotes,

author = {Clarence W. Wilkerson and Jr.},

title = {Lab Notes on the exceptional Lie group E8 at the prime 2},

year = {}

}

### OpenURL

### Abstract

This is an account of the author’s use of computer algebra tools to explore the structure of the maximal elementary abelian 2-subgroups of the exceptional Lie group E8. The principal result obtained thus far by these methods is that any rank 8 connected 2-compact group (BX,X) with Weyl group isomorphic to that of the exceptional Lie group E8 has its normalizer of the maximal torus isomorphic to that of E8 at the prime 2. Similar results hold for the comparison of possible exotic forms of G2, DI(4), F4, andE7/Z(E7) to the standard forms. Corollaries of this result include that the Krull dimension of the mod 2 cohomology of such BX is 9 and that the cohomology ring is not Cohen-Macaulay. The proof follows from (1) calculations of the ambient cohomology group H2 (BW(G),TG) that classifies extensions 1 → TG → NG(TG) → W(G) → 1 and the (2) discovery of subgroups in common between the “real ” E8 and possible W-clones X which are large enough to detect the kinvariant.