A Poincare-birkhoff-witt Theorem for Quadratic Algebras with Group Actions

  title={A Poincare-birkhoff-witt Theorem for Quadratic Algebras with Group Actions},
  author={Anne V. Shepler and Sarah Witherspoon},
Braverman, Gaitsgory, Polishchuk, and Positselski gave necessary and sufficient conditions for a nonhomogeneous quadratic algebra to satisfy the Poincaré-Birkhoff-Witt property when its homogeneous version is Koszul. We widen their viewpoint and consider a quotient of an algebra that is free over some (not necessarily semisimple) subalgebra. We show that their theorem holds under a weaker hypothesis: We require the homogeneous version of the nonhomogeneous quadratic algebra to be the skew group… CONTINUE READING

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