PBW-deformations of \(N\)-Koszul algebras.

DOI10.1016/j.jalgebra.2005.08.032zbMath1159.16026arXivmath/0505570OpenAlexW1985591189MaRDI QIDQ852664

Jon Eivind Vatne, Gunnar Fløystad

Publication date: 15 November 2006

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505570

zbMATH Keywords

tensor algebrasassociated graded algebras\(N\)-Koszul algebrasYoneda algebrasPoincaré-Birkhoff-Witt deformationshomogeneous algebrasArtin-Schelter algebras

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Deformations of associative rings (16S80) Quadratic and Koszul algebras (16S37)

Related Items

Koszul calculus for \(N\)-homogeneous algebras ⋮ Nakayama automorphisms of PBW deformations and Hopf actions. ⋮ Realization of PBW-deformations of type \(\mathbb{A}_n\) quantum groups via multiple Ore extensions ⋮ Deformations of Koszul Artin-Schelter Gorenstein algebras. ⋮ PBW-deformations of quantum groups ⋮ Symmetries in connected graded algebras and their PBW-deformations ⋮ The General PBW Property ⋮ Generalizing the notion of Koszul algebra. ⋮ HOMOGENEOUS PBW DEFORMATION FOR ARTIN–SCHELTER REGULAR ALGEBRAS ⋮ PBW deformations of a Fomin-Kirillov algebra and other examples ⋮ PBW-deformations and deformations à la Gerstenhaber of \(N\)-Koszul algebras. ⋮ Deformations of Quadratic Algebras with Antisymmetric Relations ⋮ THE CURVED A∞-COALGEBRA OF THE KOSZUL CODUAL OF A FILTERED DG ALGEBRA ⋮ Unnamed Item ⋮ Poincaré-Birkhoff-Witt Deformations of a Class ofN-Homogeneous Algebras ⋮ Hochschild dimension for graded algebras. ⋮ Poincaré Duality for Koszul Algebras

Cites Work

• Higher symplectic reflection algebras and non-homogeneous \(N\)-Koszul property.
• Graded algebras of global dimension 3
• The Koszul property in affine semigroup rings
• Nonhomogeneous quadratic duality and curvature
• Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type
• Koszul and Gorenstein properties for homogeneous algebras.
• Koszul Resolutions
• Introduction to \(A\)-infinity algebras and modules
• Koszulity for nonquadratic algebras.