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      A Morita theorem for modular finite W-algebras

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          Abstract

          We consider the Lie algebra \g of a reductive algebraic group over a field of positive characteristic. To each nilpotent e\in \g it is possible to attach a certain filtered, associative algebra \hat{U}(\g,e) known as a finite W-algebra, defined as the opposite endomorphism ring of the generalised Gelfand-Graev module associated to (\g, e). This is shown to be Morita equivalent to a certain central reduction of the enveloping algebra of U(\g), provided the characteristic of the field is very large. This result is an analogue of Premet's famous Morita theorem for restricted finite W-algebras, and leads immediately to a modular version of Skryabin's equivalence.

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          Journal
          2015-05-14
          2015-06-16
          Article
          1505.03896
          34f55f98-8ae6-4d5c-8296-1d7a07106767

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          14 pages. Added a section on the modular version of Skryabin's equivalence & simplified some arguments
          math.RT

          Algebra
          Algebra

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