Braided Picard groups and graded extensions of braided tensor categories

• Alexei Davydov ^[1] ; Dmitri Nikshych ^[2]
  1. [1] Ohio University

     Ohio University

     Township of Athens, Estados Unidos

     
  2. [2] University of New Hampshire

     University of New Hampshire

     Town of Durham, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 4, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00670-1
• Enlaces
  • Texto completo
• Resumen

  • We classify various types of graded extensions of a finite braided tensor category B in terms of its 2-categorical Picard groups. In particular, we prove that braided extensions of B by a finite group A correspond to braided monoidal 2-functors from A to the braided 2-categorical Picard group of B (consisting of invertible central B-module categories). Such functors can be expressed in terms of the Eilnberg-Mac Lane cohomology. We describe in detail braided 2-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories.