Tannaka-Krein duality for compact groupoids I, Representation theory

• Autores: Massoud Amini
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 1, 2007, págs. 78-91
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.09.015
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• Resumen

  • In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous representations of compact groupoids. We show that irreducible representations have finite dimensional fibres. We prove Schur's lemma and Peter-Weyl theorem for compact groupoids.