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Poincaré-Birkhoff-Witt Bases for Dioperads

  • Author(s): Katz, Adam
  • Advisor(s): Gan, Wee Liang
  • et al.
Abstract

We define a functorial way to turn a cyclic operad into a dioperad. Bergman's Diamond Lemma and Hoffbeck's PBW bases for operads are generalized to the setting of dioperads. We use these results to show that the induced dioperads from the cyclic operads

Com and Lie are Koszul.

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