Poincaré Duality for Koszul Algebras

Abstract

AbstractWe discuss the consequences of the Poincaré duality, versus AS-Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poincaré duality property implies the existence of twisted potentials which characterize the corresponding algebras while in the case of quadratic linear Koszul algebras, the Poincaré duality is needed to get a good generalization of universal enveloping algebras of Lie algebras. In the latter case we describe and discuss the corresponding generalization of Lie algebras. We also give a short review of the notion of Koszulity and of the Koszul duality for \(N\)-homogeneous algebras and for the corresponding nonhomogeneous versions.KeywordsQuadratic PartDifferential AlgebraHochschild CohomologyKoszul ComplexCochain ComplexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.