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SUMMARY:Madeleine Jotz Lean (Univ. Göttingen)
DTSTART:20210326T130000Z
DTEND:20210326T150000Z
DTSTAMP:20260423T022834Z
UID:DQSeminar/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DQSeminar/6/
 ">Transitive double Lie algebroids via core diagrams</a>\nby Madeleine Jot
 z Lean (Univ. Göttingen) as part of Deformation Quantization Seminar\n\n\
 nAbstract\nThis talk begins by explaining Brown and Mackenzie’s equivale
 nce of locally trivial double groupoids with locally trivial core diagrams
  (of groupoids). Then it establishes an equivalence between\nthe category 
 of transitive double Lie algebroids and the category of transitive core di
 agrams (of Lie\nalgebroids). The construction of this equivalence uses the
  comma double Lie algebroid of a morphism\nof Lie algebroids\, which is in
 troduced as well. The proofs of the results in this talk rely heavily on\n
 Gracia-Saz and Mehta’s equivalence of decomposed VB-algebroids with supe
 r-representations\, and\nthey showcase the power of this recent tool in th
 e study of VB-algebroids. Since core diagrams of\n(integrable) Lie algebro
 ids integrate to core diagrams of Lie groupoids\, the equivalences above y
 ields\na simple method for integrating transitive double Lie algebroids to
  transitive double Lie groupoids.\nThis is joint work with Kirill Mackenzi
 e\, who sadly passed in 2020.\n
LOCATION:https://researchseminars.org/talk/DQSeminar/6/
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