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Lie algebroid cohomology and Lie algebroid extensions

144   0   0.0 ( 0 )
 Added by Ugo Bruzzo
 Publication date 2017
  fields
and research's language is English




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We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of extensions 0 --> L --> E --> Q --> 0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.



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