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Characterization of the Mod 3 Cohomology of the Compact, Connected, Simple, Exceptional Lie Groups of Rank 6
Author(s) -
Kono Akira,
Nishimura Osamu
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002121
Subject(s) - mathematics , steenrod algebra , cohomology , homotopy , eilenberg–maclane space , pure mathematics , lie algebra , mod , algebra over a field , rank (graph theory) , discrete mathematics , combinatorics , homotopy group
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. 2000 Mathematics Subject Classification 57T05, 57T10, 57T25.