PBW-deformation theory and regular central extensions

DOI10.1515/CRELLE.2007.065zbMath1147.16022arXivmath/0603375OpenAlexW1965800456MaRDI QIDQ5387204

Brad Shelton, Thomas Cassidy

Publication date: 8 May 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603375

zbMATH Keywords

presentationsdeformations of ringsfiltered ringsfree rings

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Deformations of associative rings (16S80) Graded rings and modules (associative rings and algebras) (16W50)

Related Items (16)

Nakayama automorphisms of PBW deformations and Hopf actions. ⋮ Realization of PBW-deformations of type \(\mathbb{A}_n\) quantum groups via multiple Ore extensions ⋮ Noncommutative Euclidean spaces ⋮ PBW-deformations of graded rings ⋮ Generalized down-up algebras revisited from a viewpoint of Gröbner basis theory ⋮ PBW-deformations of quantum groups ⋮ Returning arrows for self-injective algebras and Artin-Schelter regular algebras. ⋮ Symmetries in connected graded algebras and their PBW-deformations ⋮ Homogenized skew PBW extensions ⋮ Poincaré-Birkhoff-Witt deformation of Koszul Calabi-Yau algebras. ⋮ The lower and upper bounds of the degree distribution of a graded algebra. ⋮ The Yoneda Algebra of a Graded Ore Extension ⋮ Generalizing the notion of Koszul algebra. ⋮ Generalized Koszul properties for augmented algebras. ⋮ Skew Clifford algebras ⋮ Poincaré-Birkhoff-Witt Deformations of a Class ofN-Homogeneous Algebras

Cites Work

• Order relations on induced and prime ideals in the enveloping algebra of a semisimple Lie algebra
• Higher symplectic reflection algebras and non-homogeneous \(N\)-Koszul property.
• Graded algebras of global dimension 3
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Deformed preprojective algebras and symplectic reflection algebras for wreath products.
• Global dimension 4 extensions of Artin-Schelter regular algebras
• Vertical components and flatness of Nash mappings
• Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type
• Noncommutative deformations of Kleinian singularities
• Koszulity for nonquadratic algebras.

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