Morita equivalence of Poisson manifolds

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Abstract

Poisson manifolds are the classical analogue of associative algebras. For Poisson manifolds, symplectic realizations play a similar role as representations do for associative algebras. In this paper, the notion of Morita equivalence of Poisson manifolds, a classical analogue of Morita equivalence of algebras, is introduced and studied. It is proved that Morita equivalent Poisson manifolds have equivalent "categories" of complete symplectic realizations. For certain types of Poisson manifolds, the geometric invariants of Morita equivalence are also investigated.

Original languageEnglish (US)
Pages (from-to)493-509
Number of pages17
JournalCommunications In Mathematical Physics
Volume142
Issue number3
DOIs
StatePublished - Dec 1 1991

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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