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CHARACTERIZATION OF THE MOD 3 COHOMOLOGY OF THE COMPACT, CONNECTED, SIMPLE, EXCEPTIONAL LIE GROUPS OF RANK 6

Published online by Cambridge University Press:  13 August 2003

AKIRA KONO  and
OSAMU NISHIMURA
AKIRA KONO
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japankono@kusm.kyoto-u.ac.jp
OSAMU NISHIMURA
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japanosamu@kusm.kyoto-u.ac.jp
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Abstract

It is shown that the mod $3$ cohomology of a $1$-connected, homotopy associative mod $3$$H$-space that is rationally equivalent to the Lie group $E_6$ is isomorphic to that of $E_6$ as an algebra. Moreover, it is shown that the mod $3$ cohomology of a nilpotent, homotopy-associative mod $3$$H$-space that is rationally equivalent to $E_6$, and whose fundamental group localized at $3$ is non-trivial, is isomorphic to that of the Lie group $\Ad E_6$ as a Hopf algebra over the mod $3$ Steenrod algebra. It is also shown that the mod $3$ cohomology of the universal cover of such an $H$-space is isomorphic to that of $E_6$ as a Hopf algebra over the mod $3$ Steenrod algebra.

Keywords

57T0557T1057T25
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 5 , September 2003 , pp. 615 - 623
Copyright
© The London Mathematical Society 2003

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