Generalizing the Notion of Koszul Algebra
نویسندگان
چکیده
We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into
منابع مشابه
K2 Factors of Koszul Algebras and Applications to Face Rings
Generalizing the notion of a Koszul algebra, a graded kalgebra A is K2 if its Yoneda algebra ExtA(k, k) is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem about K2 factor algebras of Koszul algebras and use that theorem to show the Stanley-Reisner face ring of a simplicial complex ∆ is K2 whenever the Alexander dual simplicial complex ∆∗ is (sequentially) Cohen-...
متن کاملKoszul Duality for PROPs
The notion of PROP models the operations with multiple inputs and multiple outputs, acting on some algebraic structures like the bialgebras or the Lie bialgebras. We prove a Koszul duality theory for PROPs generalizing the one for associative algebras and for operads.
متن کاملOn Koszul Property of the Homogeneous Coordinate Ring of a Curve
This paper is devoted to Koszul property of the homogeneous coordinate algebra of a smooth complex algebraic curve in the projective space (the notion of a Koszul algebra is some homological refinement of the notion of a quadratic algebra, for precise definition see next section). It grew out from the attempt to understand methods of M. Finkelberg and A. Vishik in their paper [10] proving this ...
متن کاملOn the Multi-Koszul Property for Connected Algebras
In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras. This notion also extends and generalizes the one recently introduced by the author and A. Rey, which was for the particular case of al...
متن کاملHomological Perturbation Theory for Algebras over Operads
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. Specifically, for an operad O, we define the notion of an ‘O-algebra contraction’ and we prove that the formulas of the Basic Perturbation Lemma preserve O-algebra contractions. Over a ground ring containing the rational numbers, we give explicit formulas for constructing an O-algebra ...
متن کامل