PBW-deformation theory and regular central extensions

Details PBW-deformation theory and regular central extensions PBW-deformation theory and regular central extensions

2006-03-15

arxiv.org/abs/math/0603375v2

Mathematics

Rings and Algebras

Scientific paper

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 $A$.

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