Unitary embeddings of finite loop spaces

  • 1 Consejo Nacional de Ciencia y Tecnología, Centro de Investigación en Matemáticas, A. C. Unidad Mérida, Parque Científico y Tecnológico de Yucatán, Carretera Sierra Papacal-Chuburná Km 5.5, Mérida, YUC 97302, Mexico
  • 2 Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, E-08193 Bellaterra, Spain
José CantareroORCID iD: http://orcid.org/0000-0001-6144-2003 and Natàlia Castellana

Abstract

In this paper we construct faithful representations of saturated fusion systems over discrete p-toral groups and use them to find conditions that guarantee the existence of unitary embeddings of p-local compact groups. These conditions hold for the Clark–Ewing and Aguadé–Zabrodsky p-compact groups. We also show the existence of unitary embeddings of finite loop spaces.

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