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

@inproceedings{Shepler2012APT, title={A Poincare-birkhoff-witt Theorem for Quadratic Algebras with Group Actions}, author={Anne V. Shepler and Sarah Witherspoon}, year={2012} }

- Published 2012

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