Picard groups of poisson manifolds

Henrique Bursztyn, Rui Loja Fernandes

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Abstract

For a Poisson manifold M we develop systematic methods to compute its Picard group Pic(M), i.e., its group of self Morita equivalences. We establish a precise relationship between Pic(M) and the group of gauge transformations up to Poisson diffeomorphisms showing, in particular, that their connected components of the identity coincide; this allows us to introduce the Picard Lie algebra of M and to study its basic properties. Our methods lead to the proof of a conjecture from [4] stating that Pic(g) for any compact simple Lie algebra agrees with the group of outer automorphisms of g.

Original languageEnglish (US)
Pages (from-to)1-38
Number of pages38
JournalJournal of Differential Geometry
Volume109
Issue number1
StatePublished - May 2018

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ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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