The classification of p-compact groups for p odd

• Autores: Kasper K.S. Andersen, Jesper Grodal, Jesper M. Møller , Antonio Angel Viruel Arbaizar
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 167, Nº 1, 2008, págs. 95-210
• Idioma: inglés
• DOI: 10.4007/annals.2008.167.95
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• Resumen

  • A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem for p odd.