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Koszul and homogeneous Koszul algebras were defined by Priddy in \cite{Priddy1970}. There exist some relations between these algebras and the skew PBW extensions introduced in \cite{LezamaGallego}. In this paper we give conditions to guarantee that skew PBW extensions over fields are Koszul or homogeneous Koszul. We also show that a constant skew PBW extension of a field is a PBW deformation of its homogeneous version.
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Suárez, H., & Reyes, A. (2017). KOSZULITY FOR SKEW PBW EXTENSIONS OVER FIELDS. JP Journal of Algebra Number Theory and Applications, 39(2), 181–203. https://doi.org/10.17654/nt039020181
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