A finite loop space not rationally equivalent to a compact Lie group

@article{Andersen2003AFL,
  title={A finite loop space not rationally equivalent to a compact Lie group},
  author={Kasper K. S. Andersen and Tilman Bauer and Jesper Grodal and Erik Kjaer Pedersen},
  journal={Inventiones mathematicae},
  year={2003},
  volume={157},
  pages={1-10}
}
We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5. 

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