Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids

  title={Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids},
  author={Theodore Th. Voronov},
We define graded manifolds as a version of supermanifolds endowed with an extra Z-grading in the structure sheaf, called weight (not linked with parity). Examples are ordinary supermanifolds, vector bundles, double vector bundles (in particular, iterated constructions like TTM), etc. I give a construction of doubles for graded QS- and graded QP-manifolds (graded manifolds endowed with a homological vector field and a Schouten/Poisson bracket). Relation is explained with Drinfeld's Lie… 

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  • A. Bruce
  • Mathematics
    International Journal of Geometric Methods in Modern Physics
  • 2019
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalization of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids, we



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