2006/03/15 by Cassidy, Thomas, Shelton, Brad
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.math/0603375
A deformation U, of a graded K-algebra A is said to be of PBW type if grU is A. It has been shown for Koszul and N-Koszul algebras that the deformation is PBW if and only if the relations of U satisfy a Jacobi type condition. In particular, for these algebras the determination of the PBW property is a \it finite and explicitly determined linear algebra problem. We extend these results to an arbitrary graded K-algebra, using the notion of central extensions of algebras and a homological constant attached to A which we call the \it complexity of A.